Good Morning sir :-) @JohnRennie

@user8718165 morning :-)

@JohnRennie Sir I want to ask you a few questions...Did you have coffee?

Give me five or ten minutes ...

@JohnRennie Suuuureeee

OK. Coffee is made! What's the question?

@JohnRennie hi can I ask a quick q?

@psa hi, yes, what did you want to ask?

I don't understand this solution

How is intensity = size x rate? The way I'm interpreting it, if size = energy and rate = frequency, then size x rate is power.

@psa Intensity and power are the same thing

I guess, up to a factor of 1/area....

@JohnRennie why does the area not matter?

what even is the physical interpretation of area in this case? some imaginary plane that the photons are crossing?

The question is oversimplified and actually a rather poor question. I guess it assumes a unit area.

felt the same way

I'm not sure it's worth exercising too many brain cells on it :-)

hahahahah

ok sounds good

@JohnRennie hi

@psa hi

Just looking for some intuition on this. So as far as I understand a quantum state is the state of a quantum object, and this can be represented by a linear combination of eigenstates. But where I get confused is that the quantum state can also be described by a wave function? So, a wavefunction is used when the domain we are working over is infinite, rather than a combination of a finite number of states?

The wavefunction is the quantum state ...

So if I represented a quantum state as a linear combination of a finite number of eigenstates (for instance in that resonance question that we did), this would be a wavefucntion?

or is what we did just an approximation?

You can choose any operator, and with that operator comes a set of eigenstates of that operator. We tend to think of eigenstates of the Hamiltonian, but we could equally well use eigenstates of the momentum operator (i.e. infinite plane waves). Then we can use the set of eigenstates as a basis for our Hilbert space i.e. write our state as a sum of our selected eigenstates.

For the momentum states we would be constructing our state using Fourier synthesis i.e. we Fourier transform the state to expess it as a sum of plane waves.

In general the state will be an infinite sum of our selected eigenstates, so any finite sum is an approximation.

In all of the above you can use the words state and wavefunction interchangeably.

Does this make sense so far?

yes

Sometimes the Hilbert space will be finite dimensional e.g. the state of a spin in an electric field contains just the two eigenstates up and down. This would be the exception rather than the rule through.

I need to work for a bit, but I'll be done in an hour if you still want to ask anything.

@JohnRennie no that was quite helpful

appreciate it!

although I might think of more questions : )

take care

@JohnRennie you there?

@Archer hi :-)

@JohnRennie can I ask you a general advice question? (can defer til later when Archer replies)

@psa yes, ask now Archer has disappeared!

OK

so, I would like to (at some point) do real theoretical physics. the nice thing is, my university has an undergraduate thesis option available so I can definitely do so in fourth year (even if it's an "easy" problem). I'm in 2nd year right now, and the programs offered at my university start to fork off after this year (into 3rd and 4th). I've been thinking about it since first year, but I still can't decide whether I should go the "physics" route or the "physics + math" route.

when I asked a potential advisor about different math courses and what courses he recommends taking, who did physics + math at the same university, he said that some of the courses you do in the combined route don't really help you in theoretical physics much (real analysis specifically).

I need to be cautious giving advice because I didn't do a theoretical course - I worked as an experimental scientist. Bear in mind that advice from me is worth roughly what you pay for it!

that's fair enough, although I do certainly value your advice! I'll keep that in mind though

Having said this, modern theoretical physics is intensely mathematical, as in you really, really need to love maths to make a career in it.

I'm still quite torn though, because many of his previous students (and people that I see who go down the theory road) seem to do the combined route. I don't know if that's just de facto where I "should" be going for what I want to do, or if that's just because people who like theoretical physics like math.

I suspect it's just because people who like theoretical physics like math.

From conversations with theoretical physicists I get the impression that maths departments take a very different view of maths from physicists, and they approach it in a different way.

So as a general rule courses given by maths departments for mathematicians are not that useful to physicists.

yeah, I really do love certain math classes (linear algebra and multivariable/vector calculus come to mind)

but I could take or leave others

like I don't really care for really intense number theoretic group theory or something like that

group theory for physicists, though, = interesting

You sound to me like a physicist not a mathematician :-)

well, that's the thing. I'd like to do research in physics, which is what they're doing. it's just that even the PI himself did the combined option, and I don't know if not taking that would somehow make it much harder for me to do the math, or if I could just figure it out on the go.

I would certainly look out for maths courses intended for physicists, as opposed to maths courses intended for mathematicians, but I'd be surprisised if you found you enjoyed doing maths for mathematicians at final year degree level.

yeah, no, I've already perused those types of courses

Have you looked at quantum field theory i.e. got a book and attempted to learn it?

there's specific ones like green's functions and calculus of variations that interest me

but not stuff like algebraic topology etc

That would be a pretty good, if somewhat brutal, introduction to how maths is used in physics.

I've very quickly glanced (keyword glanced) at Peskin and Schroeder

if somewhat brutal haha

Maybe set aside a couple of days and have a real go at Peskin and Schroeder or Schwartz.

I can show you the type of research that the PI who I'm interested in does (he works in quantum gravity specifically)

alright

arxiv.org/pdf/1609.00026.pdf this is an old-ish (3 years now) set of lectures he did, basically with the idea of building spacetimes from entanglement entropy

I'm very interested in QG (or anything related to it).

The exciting developments in previous decades have lead nowhere and people are casting around for ideas with any clear guiding principles.

It has also got exceedingly mathematical.

You think it's a dying field?

I'm not sure I'd go that far, but I suspect jobs in QG will be few and hard to come by.

I do definitely understand what you mean there. I can't say you're wrong.

The QG people at UBC have this "talk" with you if you have a desire to do research with them.

As in, there are no jobs.

And you'll be competing for those few jobs with some real uber-maths nerds.

I get that... But I'd like my taste of the pie at least for an undergraduate thesis. It's been something I've had an interest in since I was quite young. I can move on after that.

In that case I'd say go for it.

I don't expect to create anything fantastical or amazing. I'd just like to be a small part of something that might one day lead to something.

I ended up working ina field that I didn't even know existed when I was an undergrad.

Which field was that?

Colloid science

I'm certainly a realist about this - but a kid can dream!

You're only in year two, and a lot can happen in the next two and a half years.

And as a general rule you'll work hardest and most successfully at the things you enjoy most.

So I guess I should probably just stay in the normal physics hons stream rather than combined?

I don't need to decide today, but it's something I need to think about.

And it's been a hard decision.

Only a tiny fraction of people who do theoretical physics degrees end up working in theoretical physics. The rest find that the skills they developed in their degrees are in great demand in all sorts of industries.

So I don't think it matters too much what you choose in the long term.

Yes - my friend Mike (who worked on AdS/CFT correspondence with the same researcher) works as a data scientist for plenty of fish now (lol)

(actually a great job apparently)

It pays a lot better than academia does, and there's a lot more job security!!!

OK, that's fair enough then

But to go back to your original question, if you don't have to decide now then don't decide now.

Procrastination can be a surprisingly effective way of dealing with things like this. By the time you do need to decide you may find you feel more clearly about what you want to do.

procrastination sounds good to me then

For now concentrate on doing what you enjoy doing. I do recommend having a go at QFT. See if the attempt to learn that affects your views.

Personally, it served only to convince me that experimental science was my thing :-)

haha

okay

although you do enjoy GR!

also, I know that Feynman was a special one, but he didn't have much of a taste for pure math and he was an excellent theoretical physicist

sometimes I wonder what he would say about the current state of things

@psa I enjoyed learning how GR worked i.e. understanding the basic principles, and that's all I've learned.

I can do basic manipulation of metrics, which is all you need to answer many of the questions on GR that get asked here, but once things get technical I'm completely lost.

This is completely the opposite of a real GR nerd because they would be fascinated by the technical details and that's exactly what I'm not interested in!

yeah, like the type of GR nerd that carries around Wald with them?

That's the one (also they have big arm muscles)

haha

The best thing about Wald is that MTW is even heavier.

@JohnRennie, Hi Sir. Is electric current scalar? I know it doesn't obey triangle/parallelogram law of vector addition. So it's not a vector for sure. A comment in the top voted answer to a question on Phy.SE says, if it's not a vector it doesn't mean it's a scalar. So what exactly is current sir, a scalar, or something else?

@Intellex you need to distinguish between current and current density.

Current density is a vector field, but current is a scalar.

@JohnRennie Ordinary current sir. I know current density is vector.

Ordinary current is a scalar

@JohnRennie But current has both magnitude and direction unlike other scalars which only have magnitude.

Is there any other quantity other than scalars and vectors to define current.

I wouldn't say current has a direction.

I think it is similar to this sir - if a particle is not positively charged it doesn't mean it's negatively charged. It might be chargeless.

Current can be positive or negative, but so can most scalars. Just having a sign does not make a quantity a vector.

@JohnRennie Thank you sir. I understand they are not vectors. But I am confused whether they must be scalars.

@JohnRennie Sir, could you please explain this statement?

Current is the integral of the current density, $\mathbf J \cdot d\mathbf A$ i.e. it is the integral of a dot product.

So it is a scalar by definition.

@JohnRennie As it's an area :)

Thank you sir

@JohnRennie Hello sir sorry I didn't respond to you. It was an integrals question... I found out the answer sir

@user8718165 cool :-)

Still thank you so much 😊

@JohnRennie what are you doing now sir?

@user8718165 trying to answer a question on the science fiction stack exchange ...

@JohnRennie wow sir...can you show me?

@JohnRennie You're great... I didn't even get the question XD

@JohnRennie Go on sir :-)

I'll have to go through my book collection in an attempt to find this. That's going to take a while ...

@JohnRennie yeah sir... you mentioned that in the comments. you read it about a decade ago ;-)

@JohnRennie Can you attempt UPSC Interview Questions?

1. Tell me about yourself? or Give a brief Introduction about yourself.

3. Tell me about your positive and negative strengths.

4. How can you drop a raw egg onto a concrete floor without cracking?

5. What will you do if I run away with your sister? (asked by the interviewer)

6. Interviewer ordered a cup of coffee for the candidate. Coffee arrived and was kept before the candidate. what is before you?

7. What happened when the wheel was invented?

8. You are driving along in your car on a wild, stormy night, it's raining heavily, when suddenly you pass by a bus stop, and you see three people waiting for a bus: An old lady who looks as if she is about to die; an old friend who once saved your life and the perfect partner you have been dreaming about. Which one would you choose to offer a ride to, knowing very well that there could only be one passenger in your car?

9. What if one morning you woke up & found that you were pregnant? ( asked to a female candidate)

10. Where Lord Rama would have celebrated his "First Diwali"?

Answers are here, but please try to answer those without answers - jagranjosh.com/articles/…