is the context of the photoelectric effect that scientists of the last few hundred years became increasingly concerned with light and its affect on matter (for example the photovoltaic effect)

Anyone know how Rayleigh-Jeans law of spectral radiance came about?

says on wiki that "In 1900, the British physicist Lord Rayleigh derived the $\lambda^{-4}$ dependence of the Rayleigh–Jeans law based on classical physical arguments and empirical facts"

Okay if anyone comes online, "He assumed that a hypothetical electrically charged oscillator in a cavity that contained black-body radiation can only change its energy in quantized steps, and that the energies of those steps are proportional to the frequency of the oscillator's associated electromagnetic wave." anyone understand what this means

The more I read about the history of physics the more I realize it's a team effort and no one man deserves more recognition than another when we have all devoted time and effort into understanding more about the world.

1800s physicists all made efforts to developing quantum theory and then one or two individuals are remembered as the "innovators" of their time lol.

So was Planck's result for spectral distribution of a blackbody derived using classical statistical mechanics? I know he assumed $E=hv$ and Rayleigh-Jean law used equipartition theorem of classical stats. The expression Planck got also had boltzmann's constant so I guess he must have but with his assumption.

@JohnRennie since you're up the earliest from what I gather, (are you in the UK because that would make sense), do you know what en.wikipedia.org/wiki/Ultraviolet_catastrophe#Solution the part "Einstein's photon had an energy proportional to its frequency and also explained an unpublished law of Stokes and.." is referencing to?

It has piqued my curiosity.

@Obliv I suspect this is Stokes' rule for fluorescence and phosphorescence, and this says the energy of the emitted light is always less than or equal to the energy of the incident light.

I will bookmark this for later, man I am so terrible with time management.

If I didn't have to study for a quiz tomorrow, then a test for calc on wednesday I'd look into this more. So much valuable information on wikipedia.. and I ignore that donation message every time :\

When I'm not broke I will finally make that small contribution.

In degenerate pertubation theory, the first correction in energy is equal to the expectation value of the disturbance operator in the unperturbed state. Do we use here the eigenstates that we find when diagonalizing the disturbance operator in the Eigenspace of a degenerate eigenvalue?

@Obliv Perhaps you don't need to feel as bad about that as you think, see e.g. this internal Wiki discussion where many users are skeptical of running these banners because they usually raise far more money than is required for running Wikipedia itself

the donations go to the Wikimedia foundation (WMF), and apparently the fraction of that that is actually used to run Wikipedia itself is a contentious issue.

especially if you don't have a lot of money, don't feel guilty about not giving it to the WMF

@ACuriousMind what's your take on sites like libgen?

@Feynman_00 Academic publishing as it exists today is evil and violating the copyright of these publishers is the right thing to do.

[Disclaimer: As a moderator on an SE site I do not handle copyright violations; copyright claims are processed by actual SE employees]

@ACuriousMind Why do you say it's evil? Just asking to feel less guilty about using libgen for few books

And also because I've been procrastinating this dilemma for a long time now

@Feynman_00 They profit off work they largely do not produce: The papers and books are written by scientists funded largely by governments or other parties unrelated to the publishers, peer-review is also provided by the scientists free of charge, and the largest share of people who pay for access to this material are again either scientists or students (usually collectively in the form of institutional libraries).

in the age of digital media, they often don't even have actual printing costs anymore, yet they make billions of dollars solely on the reputation of journals to which they contribute nothing worthwhile - they just own them.

even if we accept that scientific knowledge is something that should be gated by access fees and copyright, this business model is deeply unethical: Sure, we can often argue about whether or not the workers for a company are receiving just wages in proportion to their labour, but in academic publishing, the most important workers in the process receive no wages at all

If anything this perspective makes me feel less of a bad person. Up to now I've considered it as a necessity i.e. I can't afford to buy every book I consult once or twice, although one could argue there are universities libraries but again they don't have any book

and almost everyone participating in this process only do does because they feel they must: Look at the rise of arXiv as a primary source for articles and how many scientists either have free links to their works on their webpages or offer to send it to people free of charge on request

no one wants to have academic knowledge gated by publishers except publishers

Well, although this might sound too simplistic I think it would be cool if people could just spread the pdf of their books on their site without needing a publisher but of course it doesn't work like that

I think most book writers would do that or at least I know some that already do

I mean...sometimes it does work like that

but this means completely opting out of the process of academic publishing and in particular opting out of the prestige that comes with publication in a reputable journal or a reputable book series

I would still say that this is the correct thing to do, but of course for anyone except a truly well-established professor with tenure there are understandable egoistic reasons not to do so

It works, yes, but most of the times the book does not receive the credit it deserves

@ACuriousMind this

I thought about this some days ago, when I was looking for a book about constrained hamiltonian systems to buy but apparently I can't find it anywhere so in that case downloading was the only option and I wondered whether I was really justified

Is it Quantization of Gauge Systems? I can't talk about Hamiltonian constraints without mentioning that book at least once :P

I admit I wanted to bait you, but no. It is actually named "Constrained Hamiltonian systems" by Hanson, Regge et al.

boo

(I don't know that book, it's probably nice)

You adviced QoGS some time ago and I might want to use that during the next semester

@ACuriousMind it's about constrained hamiltonians and gauge theories, it has to be :P

Dang, I feel like doing (almost) only maths lately: lie theory, differential geometry and everything except QFT is getting frustrating

QFT is lame

@Slereah I'll take GR next semester

The only thing that makes me sad about QFT is the "effective field theory" stuff

what's sad about EFT

presumably the realization that QFT is not (necessarily) the pristine "fundamental" theory a certain brand of theorist tries to sell it as :P

What ACM said

Not sad like "it sucks", more like "ooooh dang"

Is a "pristine fundamental" theory even possible?

That's the sad part

maybe, but the hard part is usually solving it to check if it is

@Feynman_00 I would argue this type of disappointment arises from an (often unconscious or unexamined) hope/belief that physics, at its "end", should turn out to be purely a priori reason: The way the world is should somehow arise from PURE LOGIC, not from something as banal as experimental facts

Yes, that's it. It's basically the "question" in the message above

Which is not a question to you all but to the world itself

I think this is a silly belief because it fundamentally misunderstands the nature of science and of physical theories, but it is an oddly common instinct among "pure" theorists (and it lurks underneath many arguments about aesthetics and "naturalness")

Turns out there is no reason why a physical theory should be true over another

you have to check it like a dirty peasant

by using rods and strings

I think every good theorist takes that at least into account but hope plays an important role in the uncertainty

Being a fundamental theory possible or not, I think it is an interesting issue to at least consider

no, you can't derive the universe on a blackboard

that's math, not physics

@ACuriousMind What I'm about to say will surely sound silly but if one excluded it a priori, what would make QFT really more fundamental than say thermodynamics?

Well you can derive thermodynamics from QFT

@ACuriousMind ACM, I'm not saying that you can nor I'm taking a stand here but I think excluding it a priori is not good enough right now

@Feynman_00 the pragmatic definition of a 'fundamental' theory is just one that produces the less fundamental theories as certain special or limiting cases

at least within its application to QFT

@Feynman_00 I used a priori above in a specific epistemological sense - 'a priori reason' are statements produced without empirical input

Natural science is about empirical input: Its core goal is to produce predictions for future empirical input. I do believe that it is ridiculous to think you could do that without priming your prediction machine with some empirical input to begin with; because how could you ever know what you need to describe/predict (like particles or stars or humans or chairs) without looking at the world and deciding what you need to model?

Even if the Standard Model had no alternative, if it - at the specific values of its free parameters that we observe - was truly the only consistent QFT you could write down, no other effective field theories or whatever, then you still wouldn't know that it models reality because how would you even know you should use a QFT to describe the world?

You can always do a "bad" physical theory that will predict anything anyway

Just have your physical theory be the set of all predicted outcomes for every possible experiments

and then just pick arbitrary values for those

this is why I don't buy naturalness arguments, and why it deeply dislike the attitude that free parameters are somehow a flaw: There's always a higher-level "free parameter" - why should this particular theory describe reality? You can't know that without having done all the experiments the theory is designed to explain!

It's not a very elegant theory but it is a simple example that it is possible to do so

I agree (how could I not) about science being about empirical input and I've never took a stand nor I said there is an easy way to counter your argument. I'm neither invalidating anything or saying that physics should only trash everything and only care about this. My point was only if that was even possible. If you ask me I don't think this is as easy as being able to just prove it true or wrong

I'm not exactly sure what you're saying

I'm saying I understand your point but I don't think I can just accept or deny the conclusion about a "fundamental" theory being nonsense, so I'm thinking about it

And I'll sure come back to this point in the future if you don't mind

if the argument is supposed to be "you can't disprove 100% that someone won't find a way to deduce the world from pure logic so people can still hope" then that strikes me as much the same kind of hope as "you can't disprove 100% that someone out there can do actual magic so it's okay if people believe in magic" :P

In fact I retained myself from saying that, didn't I? :P

That kind of argument could also work to "counter" atheists so I would't really use it

@Feynman_00 well, but you were either heavily implying it or I didn't understand what you were trying to say

@ACuriousMind hey :-)

I'm here to ask what are the rules to be followed to choose a proper gaussian surface while calculating electric flux? Can anybody here help me with this?

@JohnRennie I think 90% the Engineering Stackexchange chat rooms are currently dead. And I'm afraid now.

@TejasDahake I'm not sure what you mean - you can calculate the flux through any closed surface, there's aren't any "rules".

Of course, often a particular choice of surface makes whatever problem you're trying to solve particularly easy, but that's specific to the problem

Hi. Suppose we have a fixed frame system (i.e is not rotating) to the earth's center and this frame is being carried along with the earth in its orbit around the sun (but is not rotating with the earth).

Something like this: imgur.com/a/EhpGOFF

Is it true that the direction of the sun always lies in the plane $IK$?

@ACuriousMind That's what the point. I'm here for the same i.e how to ensure that I've choosen a correct gaussian surface while solving.

I am trying to see if the expression derived from this problem is correct in other cases: imgur.com/a/iTy77dk

@TejasDahake apart from a general observation that the surface often respects the symmetries of the situation (e.g. if the situation has cylindrical symmetry a good choice of surface is often a cylinder), there isn't really much to say about this in general

@Odestheory12 the orbit of the earth lies in a plane, and if you choose the coordinate system such that your I and K span that plane, then the direction towards the sun will always lie in that plane

I would like to know what values it does take during a year.

I tried to look for "angle between the sun and the equator" and I am not sure if $\sigma$ is the "latitude of the sun" or not

@ACuriousMind My teacher said that, you will be able to choose a proper gaussian surface when you'll gain a proper experience in this field so you can just leave that portion And surprisingly the same question related to this topic was included in my exam a couple of days prior.

And that thing paralysed My brain very brutally during the exam

@Odestheory12 the Earth's axis is tilted w.r.t. to its orbital plane, the IK plane is not the plane of the equator

Oh I see, that was my confusion.

see e.g. ecliptic and celestial equator

Oh wow

There is a whole 24 hours day with the sun always visible

When the angle $\sigma$ is the same than the colatitude

yes, that's what the polar circles are - ignoring atmospheric effects, you'll have at least one day where the sun never sets and one where it never rises if you're closer to one of the poles than the polar circles

so if I understood the image correctly, the angle of the sun with $\mbox{I}$ goes from -23.4 to 23.4 right?

(i.e the $\sigma$ in my problem)

yes

note that that is - within rounding - the value of the axial tilt I mentioned

Thanks this is pretty interesting

@ACuriousMind and just an another question. By the way why are the planetary orbits elliptical? I'm asking this because people gives different reasons for this some says that the planet's path is deflected from a perfect circle when a heavy celestial body passes from right next to that planet which suddenly gives them a gravitational pull. Another reason someone gives here is something related to conservation of angular momentum.

And the reason that my teacher explained it to me is that when the big bang was happened then all the planets and masses emerged with different velocities and since it was not a 'perfect match' with the velocity needed to keep an object revolving around a heavy object in a perfectly circular orbit, then the planetary orbits gained the shape of eclipse.

Yes, the latter: A circle is just a very special kind of ellipse. The general solution for an orbit is an ellipse - you need very special initial conditions to make it a circle. Now, the initial conditions for planets aren't exactly "random", but there is no reason for them to be of the kind that produces perfect circles so...they aren't circles

Noob question here: we're studying supersymmetry. we are going over susy lagrangian and the Wess Zumino model. We also studied an example of a non renormalizable theory with a particular for of the Kahler potential. Exapanding it we got non canonical kinetic terms, and this because the Kahaler potential induces a curved field manifold. In the WZ model instead the kinetic terms were canonical

so I'm thinking, is the Kahler potential of the WZ model should flat?

Can we compute some scalar curvature like we do for a generic spacetime manifold?

@john yes, the canonical choice for the Kähler potential in WZ(W) models is flat

But the problem is that ellipse has a very sharp radii at both apogee and perigee which means something is going very different at these point because if the radius gets shorter then there is may be an increment in the centripetal force or increment in the magnitude of velocity of an object but I think they both are not the cases here which are making the radius shorter at these points.

because if look at the apogee of the orbit which is far away from the sun (if we take an example of sun and earth) then the force should be decreased and the radius should be increased.

And same thing goes with the speed of the earth i.e the speed must be decreased being the energy is conserved

@TejasDahake yes, the planets are faster at the points of the ellipse that are closer to the sun

there is no problem here - at each point the only force that acts is the gravitational force from the sun

Then why the radius is shorter at the point which is far away from the sun?

what do you mean by the radius being shorter?

an ellipse doesn't have just one radius

By radius I mean

The radius which ellipse has at the farthest and the nearest point

From the sun

I'm just talking about the points 1 and 2 here as shown in the image

and what is the question?

Let me be more clear

You are saying that at point 2 the Gravitational force is stronger that is why the radius is shorter right?

not exactly, no

I mean, it is a tautology to say the gravitational force is stronger the closer you're to the sun

that's just how gravity works, nothing to do with orbits as such

Then what is the reason for being these to points (point 1 and 2) so sharp?

what do you mean by "sharp"?

By sharp I mean that if you draw a circle considering that point (lets say point 2)

The radius will come out to be very small

As compared to the other points on ellipse

I don't understand what you mean by "a circle considering that point", nor why drawing that circle has anything to do with physics

Sorry for this thing that I've no proper wordings to explain my feelings properly :-( but I'm trying my best

the circle you should compare this to is the circle with the sun as center that passes through point 2

that's the only perfect circle orbit possible for a planet that passes through point 2

when you draw it, you'll see that the ellipse is steeper than that circle, i.e. the planet on the ellipse is deflected more by the sun than the hypothetical one on a circular orbit

this is because the planet on the ellipse is slower at point 2 than it would have to be to achieve circular orbit

Okay let's just leave it for now, I'll come back with a proper explanation to my statements again.

No that's not what I'm really asking

I'll be there again with a proper explanation to my statements don't worry :-)

squack

Who let this goose in here? It's the h-bar for crying out loud.

honk !

it's probably just trying to complete some (relatively) harmless prank, if Untitled Goose Game has taught me anything

Lol that was my first thought as well, might be my favorite protagonist in a video game.

While I have you here... @ACuriousMind do you know the motivation for SR? I have somewhat of an idea that Maxwell developed the idea of EM waves through all of the work in electricity and magnetism in the earlier half of the 1800s and before.

So 1862-64 and on physicists had the idea of light as EM radiation but why did Einstein develop SR?

I also am aware that he took the quanta of an oscillatory physical system described by Planck and extended it to the idea of photons of light in 1905. That same year he apparently developed SR? Not sure how they fit together.

they don't, really :P

I vaguely remember reading something in my textbook about spherical wavelets in the SR chapter but I can't tell if that was imagined lol

physicsts before SR were well aware that something in electrodynamics was weird

Maxwell's equations predicted a constant speed for EM waves in vacuum, but...they didn't say in which frame

so the first attempt to get around this was to say, okay, it's not vacuum, it's just an "aether" medium we can't yet detect, and the speed is just the speed in the rest frame of that medium

but then experiments like Michelson-Morley were not able to detect any of the effects that should result from such a medium

Ohh

SR - for all the weirdness around time dilation and length contraction - resolves this issue very easily: The speed from Maxwell's equations is the same in all frames, that's why the equations don't need to specify one!

what do yall think is the most unexpected connection between two concepts in physics

I talked about this idea for SR to antimony just yesterday

I'm not sure but I have a feeling in this next chapter I will have a good contender. I have to take quiz on photons/matter waves and stuff @SillyGoose but I think you'd have to ask the physicists that developed theories and gauge their surprise because when I read physics I feel like it makes more sense rather than the people who developed the ideas.

something i'm blanking on. how do you write down projection operators for states of a particle in a box?

oh. it's just $\psi(x)\to \int \phi_n(x')\psi(x')\,dx' \cdot \phi_n(x)$

doy

i.imgur.com/6AudyvU.png sometimes you just gotta work with the data you have lol

I'm having an issue with this problem i.imgur.com/r2QLTYc.png

I don't get how I could find C) , the time it takes for this to happen.

nvm figured it out

I have finally found the h-bar. i.imgur.com/quhC8hv.png

it turns out it wasn't a bar/pub after all.