The h Bar

Morning :-)

user228700

@JohnRennie It turns out that my last exam is in fact, on the 27th and not the 21st of May. Meh, 6 more days.

@Kaumudi.H JEE ?

user228700

6:11 AM

No, NEST.

What is that?

Googles

user228700

^ Please do.

@Kaumudi.H didn't the 21st clash with something. Your birthday? Or am I mixing you up with someone else?

nestexam.in

I see

Good

Never heard of it

user228700

@JohnRennie No, the 2nd of April clashed with my birthday, which is on the 1st. This is another exam.

6:13 AM

Ah

@Kaumudi.H Is NISER a good institute in India ?

Is it like IISER ?

user228700

@anonymous Presumably, yes, it is, although I don't quite know the exact differences b/w NISER and IISER. My best friend is studying in IISER--I will ask him and let you know, if u want. Do you?

Okay. I think even I should give the NEST then. Looks good. But it is a very new institute it seems.

Is in this the maximum amplitude(i.e 10mm) of sinusodial will always be at x =2,4,6,8 .....

Or it will be at every position

Can somebody help me in this

@help Can you clarify what you are asking. What does your diagram show? A propagating pulse?

6:18 AM

Two propagating waves

@help If it is a moving wave then the position of amplitude will vary with time.

That is sinusodial and rectangular

@Kaumudi.H Yes, if you could let me know that's good. Thanks.

@anonymous so at every position on x axis the maximum y axis would be 10 mm

@help yeah

6:21 AM

Then how can we find its displacement at a given time

For both sinusodial and rectangular

user228700

@anonymous Sure.

user228700

@JohnR: For how much longer will u be around today? (::Smiles sheepishly::)

All morning. Another six hours or so.

Though I may have to dash out for an hour at some point.

user228700

Phew. Oh, OK.

@JohnRennie could you help me in that

6:26 AM

@help I don't understand what you are asking. It looks as if you have a sine wave pulse moving to the right and a top hat pulse moving to the left. Is that correct? If so are you adding them?

Yes

@help For sinusoidal use the equation $A\sin(wt-kx+\phi)$ where $w=2\pi f$ and k is $\frac{2\pi}{\lambda}$. $f\lambda$ is equal to velocity of the wave i.e. $1ms^{-1}$.

G'day mates :-)

@anonymous ok

@help the maximum of the sine pulse will move smoothly to the right i.e. it will pass through every point. Likewise the top hat pulse. As they meet the maximum will rise to 20mm as the amplitudes of the pulses add.

@Pissedofflayman Morning :-)

@Pissedofflayman Australian this morning? :-)

6:34 AM

@JohnRennie but for example if we have to find at x=9 then how can we find it

At time =8 sec

If both are moving with 1m/s in opposite direction

@help At time zero the sine pulse is centred at $x=2$ and the hat pulse is centred at $x=17$. Yes?

user228700

Speaking of Australia, I wonder where the heck @Kenshin is!

@JohnRennie what is displacement of hat pulse at x=16

@JohnRennie yes they are centred at that positions

@help And they both move at 1m/s so at time $t=8$ the sine pulse is centred at $x = 2 + 8 = 10$ and the hat pulse is centred at $x = 17 - 8 = 9$.

@JohnRennie yeah

6:40 AM

@help And you have to add them together to get the total amplitude. You'll need to write an equation for the amplitude of the sine pulse. The amplitude of the hat pulse is easy because it's just zero outside the pulse and 10 mm inside it.

@JohnRennie as said by @anonymous the equation of sine is Asin(wt-kx) . But here how can we find w and k

Suppose we leave out the time for a moment, and just consider the $x$ coordinate.

Ohk

A sine wave starts at zero when $x=0$, rises to a maximum at $x=\pi/2$ and falls to zero again at $x=\pi$. Yes?

Yes

@JohnRennie it is a general case

6:47 AM

And your wave is a maximum at $x=2$ and falls to zero at $x=4$. So you need $-k.2 = \pi/2$ and $-k.4=\pi$. OK so far?

user228700

Dammit, @help has hijacked my position! :-| (I'm only kidding, of course)

@JohnRennie is this at t=0

@Kaumudi.H which position?

Q: Do external fields escape from a black hole

0

Suppose there is a heavily charged body that passes by a black hole by remaining outside the event horizon all the time but close enough so that its electric/magnetic field enters the event horizon. Suppose the charged body moved fast enough and escapes the black hole to a large distance. Now w...

black-holes event-horizon

Classically should be fine, quantum mechanically however (i have no idea)

@help we're ignoring time for now so just leave out the time term.

Q: Why is Bernoullis Isentropic

0

I have trouble understanding why we classify an inviscid adiabatic incompressible flow along a streamline as isentropic Thermodynamic definition $$dS = dQ/T$$ Adiabatic Invsicid $$dQ =0= dS$$ So no heat added or lost no change in entropy. From Boltzman I am less clear how is it possible tha...

thermodynamics entropy bernoulli-equation non-equilibrium

6:52 AM

@JohnRennie fine

An example where we need tpg2114

@Secret I think that just means we take an adiabatic system

I am not very familar how fluids work because my undergrad course had not covered fluid mechanics let alone the thermodynamics of it

user228700

I've a really quick question. I'm supposed to find the electric field intensity at a point due to an infinite sheet with thickness $t$ with uniform volume charge density $\rho$ as a function of $x$ from the plane as 1) $x \le t/2$ and 2) $x \ge t/2$. My question is this: Exactly what do these different cases mean?

user228700

OK, another way to ask the same question is, where is the origin from which we are measuring $x$? My textbook says "distance from symmetry plane"...

7:01 AM

@Kaumudi.H Take an infinite sheet and view it from the side (cross section view). It will look like a rectangle ? Right? The line of symmetry of that rectangle denotes the symmetry plane of the sheet.

user228700

Oh, wow, I wasn't aware of this. Thanks.

@anonymous in that how can we find w and k

@help Just find frequency of wave and wavelength of wave and then follow my previous comment.

$w=2\pi f$ and $k=2\pi/\lambda$

@anonymous does wavelength is 4

And @anonymous frequency is also 4

Wavelength is double of 4.

Wavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats, and thus the inverse of the spatial frequency. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. Wavelength is commonly designated by the Greek letter lambda (λ). The concept can also be applied to periodic waves of non-sinusoidal shape. The term wavelength...

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example, if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second (that is, 60 seconds divided by 120 beats). Frequency is an important parameter used in science and engineering to specify the rate of oscillatory...

7:06 AM

@anonymous ohh , so both will be 8

yes

@Kaumudi.H I guess $x=0$ means the midpoint of the sheet i.e. inside the sheet.

So $|x| < t/2$ is inside the sheet and $|x| > t/2$ is outside it.

@anonymous hence at x=9 and t =8 sec displacement of sine is $-1/\sqrt 2$ cm

user228700

@JohnRennie Riight, OK. U've put it better than my textbook has, really--my textbook didn't put the absolute value sign, which was confusing and I was just about to ask about it...

user228700

@JohnRennie U just guessed this?

7:13 AM

@Kaumudi.H an educated guess based on (too many) years doing electrodynamics problems. It seems a reasonable interpretation though, otherwise why would then make the deistinction between less than and greater than $t/2$.

(sorry to interrupt)
What is the difference between matter and energy?

user228700

@JohnRennie Right, OK.

@DHMO The question is meaningless unless you define what you mean by energy

user228700

@JohnR: U're on a roll today :-P

> In physics, energy is a property of objects which can be transferred to other objects or converted into different forms but never created or destroyed.

And no, I can't define energy.

7:14 AM

@help I'm a bit busy now. It should be okay if you checked your calculation. See this graph desmos.com/calculator/zanpks2qo0

@DHMO Are you thinking of situations like a particle and antiparticle annihilating?

@JohnRennie I'm just thinking generally. You can use that as an example though.

Q: What keeps mass from turning into energy?

@DHMO Have a quick read through:

46

I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force holding a subatomic particle together? What keeps mass in it's state? I hope this is not a silly q...

special-relativity energy mass mass-energy

and see if that helps define what you are asking ...

@JohnRennie In my head I have an understanding that is probably wrong:

matter is energy confined to a region of space, or in other words, matter is trapped energy...

No, I'm afraid not.

7:17 AM

Thanks @anonymous @JohnRennie

Have a read through my answer to the question I linked above ...

I did

what is energy though

For fundamental particles energy means kinetic energy

hmm...

Then what on earth is the "energy" of an electron in the 2s orbital of hydrogen atom?

@DHMO this will get a bit complicated. How long have you got? :-)

7:23 AM

quite long

OK. For an electron in some charged environment (which could be an atom or anything charged) we consider the kinetic energy of the electron and its potential energy.

So we have two apparently different types of energy, though they interconvert.

OK so far?

yes

Our fundamental theory of particles is quantum field theory. But in QFT there is no concept of potential energy. Only kinetic energy.

When we do the maths to calculate what happens when two charged particles interact we do it by considering the interaction to be due to virtual particles. These virtual particles carry the momentum and kinetic energy that produces the interaction.

Thougn I must emphasise that virtual particles are a computational device. They don't actually exist. They are just a way of doing the maths.

So the potential energy emerges in a scarily complicated way from the quantum field theory calculations.

Eh, alright...

@JohnRennie really? That sounds... odd (but maybe I'm just tired)

7:31 AM

@DavidZ as I'm sure you're well aware I'm a QFT beginner and highly likely to be wrong or confused, but I think what I said is correct.

@JohnRennie So how is "mass" defined in QFT ? Anything having kinetic energy is called mass ? It seems like we are stuck in a loop. To define "mass" we need to use the concept of "kinetic energy" and to define "kinetic energy" we need to assume something called "mass" exists.

@anonymous In QFT the fundamental objects are the quantum fields, and these behaviour of these fields is described by the action.

The mass appears as a term in the Lagrangian density for the field.

@JohnRennie oh, I tend to assume everyone else knows everything else. But we have things like the Higgs potential, which is a potential energy, I thought.

I mean, yes, it is just a combination of fields, but still it plays the role of potential energy

@anonymous The total energy of the particle that appears as an excitation of the field is given by the equation: $$E^2 = p^2c^2 + m^2c^4 $$ where $m$ is the mass term that appears in the Lagrangian andf $p$ is the momentum.

If the mass is zero, e.g. like a photon, we get $$ E^2 = p^2c^2 $$ so there is still a total energy.

@DavidZ hmm, that's the energy of the field. Is that really a potential energy?

I would say so

7:37 AM

Possibly, though I was thinking of PE in the context of two particles interacting.

Yeah, it is a little bit different from the way classical PE works

This might be one of those cases where people could argue over terminology when they're actually talking about the same thing, it's just not clear until you go to the math

Not that I have any particular motivation to get into an argument

If you're calculating the scattering of e.g. two electrons there isn't a potential energy of the two particles in the sense it exists in classical mechanics.

Some just live to argue :-)

@JohnRennie yeah, that seems like a fair description

@DavidZ I'm in no position to argue :-) If I've got the wrong end of the stick I very much want to be told so!

7:40 AM

I do think it's just a terminology thing

@JohnRennie The common definition of quantum field (from wiki) is : "the interaction of two separate physical systems (as particles) is attributed to a field that extends from one to the other and is manifested in a particle exchange between the two systems." So does that mean even "mass" of a particle is a result of particle exchange between two systems ? But then again do the exchanged particles have no "mass" ? It seems a convoluted logic... @JohnRennie

@DavidZ that's what I was really getting at. This started by trying to explain what the potential energy of the electron in a hydrogen atom means.

@anonymous no. The mass is a fundamental property of the field.

@JohnRennie How do you define a "field" ?

When I say a field I mean a quantum field.

This isn't a field like e.g. the electrostatic field. It's an operator valued field so it's a mathematical object. The physical meaning of the quantum field is open to debate.

With a definition @anonymous :P

7:44 AM

@DHMO: this has kind of veered away from your initial question ...

It seems like we apply mathematics to things which are not even imaginable (like a quantum field) to explain the real world phenomena like "mass" and "energy". Strange but interesting :)

@anonymous All of physics is using mathematical objects to describe reality (whatever reality means). What is a wavefunction if not a mathematical object that describes some real system?

2

We introduce an arbitrary mass term into a wavefunction, so why shouldn't we do the same for a quantum field?

@JohnRennie so let's go back to the original question...

@DHMO OK, though I've forgotten where we got to ...

BTW in about ten minutes I have to get back to work for about half an hour.

you said that energy is used to create electrons in qft

i have another question if you don't mind

why can only orbitals of allowed symmetry overlap?

7:53 AM

@DHMO all orbitals overlap in space, though they may add or subtract.

Are you thinking about orbitals overlapping in chemical bonding?

yes

Can you give an example where symmetry stops orbitals from overlapping? I ask because I'm trying to clarify what you are asking.

you know, in the MO diagram of dioxygen, s orbitals and p orbitals don't overlap (or just to a small extent)

The $s$ and $p$ orbitals do overlap.

But remember that $p$ orbitals have positive and negative regions, so the total overlap may be zero i.e. the +ve and -ve bits cancel each other out.

and we call this situation "not overlapping" because the overlap term is zero

i understand this is quite misleading lol

7:58 AM

OK, it's a matter of terminology what we call it but that doesn't matter.

Whether the total overlap is zero or not just depends on whether the positive and negative parts of the $p$ orbital cancel out.

why must the number of MO equal the number of AO?

4 orbitals of oxygen and 4 orbitals of oxygen make 8 orbitals of dioxygen

@DHMO this is only true in an approximation called the linear combination of atomic orbitals or LCAO.

It's an artefact of the maths used in that approximation.

dioxygen doesn't actually have 8 orbitals?

Dioxygen has an infinite number of molecular orbitals.

Just like an atom has an infinite number of atomic orbitals.

i know

i'm talking about n=2 right

8:02 AM

For doing calculations it's often convenient to represent the MOs as being made up from a combination of atomic orbitals, but this is just a computational device. MOs aren't really just a combination of the AOs.

I have to get back to work I'm afraid. Back in about half an hour.

i think the next line would be that spdf is only for hydrogen. helium AO isn't actually spdf

In multielectron atoms atomic orbitals don't exist at all. They appear as a result of an approximation called the central field approximation. Isn't quantum mechanics fun? :-)

do MOs have quantum numbers?

i dont think that AOs dont exist...

Q: Do electrons in multi-electron atoms really have definite angular momenta?

6

Since the mutual repulsion term between electrons orbiting the same nucleus does not commute with either electron's angular momentum operator (but only with their sum), I'd assume that the electrons don't really have a well-defined angular momentum (i.e., they do not occupy a pure $\left|lm\right>...

quantum-mechanics electrons physical-chemistry atoms atomic-physics

Also:

1

Q: Aufbau principle in modern quantum theory

What is the rigorous definition of the Aufbau principle and the mathematical model used for its description? From Wikipedia, we have that the principle postulates a hypothetical process in which an atom is "built up" by progressively adding electrons. For modeling the postulate, we use the Made...

quantum-mechanics atomic-physics pauli-exclusion-principle quantum-chemistry

I see

then why do n AOs give n MOs in LCAO?

8:19 AM

It's an approximation, not reality.

do MOs have quantum numbers?

why is that a good approximation?

user228700

8:35 AM

@Bakarka: Hi. Quick question: are u a polyphasic sleeper?

@Kaumudi.H I am. (Hope I am not interrupting ). Triphasic to be more particular.

@Kaumudi.H Nah. Also, you spelled my name wrong so it didn't ping.

user228700

@anonymous Wow, that's insane. For how long does one of ur "sleep periods" last?

2 hours each. 3 hours max.

user228700

@BalarkaSen Oh, crap. Sorry. I asked only because u were active at 3 AM on the MSE chat the other day.

8:44 AM

I have been practising biphasic sleep for several years. Now I have switched to polyphasic.

@Kaumudi.H

user228700

@anonymous Oh, I see. And u feel totally refreshed, no adverse effects, etc.?

Yeah, I have a more serious problem that my sleep cycle can get permanently delayed if I don't go to bed early, which leads to insomnia etc etc.

user228700

@BalarkaSen Oh, I see, that sucks :-|

@Kaumudi.H I basically sleep when I am absolutely exhausted. So it takes be under 1 minute to fall asleep :). Initially for a few months you will find it very difficult. It is refreshing and I haven't noticed any side effect as such. But the crux is in total you should sleep atleast 6hrs in one day.

I usually reboot it after it's ridiculously messed up by delaying sleep for 24 hours and then waking up the next day. It worked ok so far.

user228700

8:47 AM

@anonymous Wow, I see. Do u plan on continuing this through college as well?

user228700

@BalarkaSen I...see.

@Kaumudi.H Maybe. Depends on the work and study pressure. Polyphasic sleep allows you to work more by reducing the energy loss you face during the later part of the day during monophasic sleep.

user228700

I...guess, but it seems just a tad impractical when you've gotta take 2 hour naps during weird parts of the day when other people might expect you to attend class/work. I guess it works if u're working/studying from home...

@Kaumudi.H I sleep between 2pm to 4pm, 12 am to 2am and between 6am to 8am. So does not intefere with school/college.

user228700

I see. The 2 PM to 4 PM might not suit college but OK...

8:54 AM

Why not try for 6 consecutive hours?

user228700

@Pissedofflayman This is the argument: (apparently)

user228700

> "Polyphasic sleep allows you to work more by reducing the energy loss you face during the later part of the day during monophasic sleep."

It's pretty hard to break your sleep cycle up into a new, polyphasic one.

user228700

@BalarkaSen Yeah. I guess you could do it during summer vacation or something when a dip in ur productivity (caused by these changes) won't affect anything.

Everyone is different

user228700

8:56 AM

^ Sure. What's ur point?

Some are night owls etc.

If you want, sure. I am happy with the one I have right now :)

user228700

@anonymous Do u plan or writing JEE?

@Pissedofflayman I don't know under what category I fall. I have practiced almost every sleep cycle :P I'm abnormal category :D

@Kaumudi.H I told you so. yes

:D

user228700

8:58 AM

@anonymous You might wanna change the timing of ur "periods", in that case...

@Kaumudi.H I know. JEE is in afternoon. I can change it in 1-2 days. I am quite flexible with sleep issues :P

user228700

Nice.

But presently this "periods" is okay for me

Anyway, if anyone is planning on practicing polyphase sleep then keep in mind that never ever keep the period shorter than 1.5 hours. That might be injurious for health.

lifehack.org/articles/lifestyle/90-minutes-sleep-cycle.html <--- interesting

user228700

I've read all the articles about sleep out there (including that one), lol :-P ($\leftarrow$ Hyperbole)

:D

bye guys :)

gotta go now

9:32 AM

(that previous deleted message is the wrong pics)

I wonder if time travel will actually screw this commutation up. Naively speaking if you have two patches of spacetime that are timelike separated, and then you proceed to identify them (basically what a CTC means), then any fields that are within this CTC is bound to be correlated to some time in its past or future as long it is within the CTC?

Therefore, for any observer within the CTC, it would seemed the future of a given field affect the field at its present time, but strictly speaking no causality is violated as the fields were already correlated right from the start due to the geometry of the CTC

OK so that was a long half an hours work ...

user228700

@JohnRennie Half an hour? Geez, I can't believe you've to work for so long even during the weekend!

A CTC can be 'created' provided any wormhole that can allow a transfer of energy momentum between the ends can be made (yes we are talking about something as small as particles, the wormhole, may be stable enough to allow these to hope between the ends (?)). One only need to take one mouth of it and gravitationally time dilate it. Then depending on how long the mouth is left time dilated, the CTC should be preceived to grow in the view of any observers
(even though the evolution of the CTC is already set to stone thus we are not really changing history here).

@Kaumudi.H It normally is only half an hour, but some mornings things just keep going wrong :-(

user228700

@JohnRennie :-( All fixed now?

9:43 AM

Yes :-)

To be fair I'm paid a lot of money for this so I can't really complain :-)

user228700

OK :-) I am procrastinating because I effing hate this chapter but there're about 60 pages to go and I've to finish by tomorrow aaaaah! :'-(

BTW I didn't buy that laptop. Someone else bid more than I thought it was worth. Oh well.

@Kaumudi.H I'll let you work then :-)

user228700

@JohnRennie Oh, that sucks :-( But you weren't that interested anyway, no?

user228700

@JohnRennie Work? If u notice, I said "I'm procrastinating" and I honestly dunno how to get myself out of this place--I just don't want to go back to the chapter (I don't like electrostatics. No. No. NO.)

@Kaumudi.H If I really wanted the laptop I would have been prepared to pay more. So yes I guess I wan't really that interested :-)

@Kaumudi.H Do something else. Put a bookmark in and jump ahead to the next chapter.

user228700

9:46 AM

@JohnRennie OK :-) Question: Siriusly, why dyou keep buying laptops..?

Actually I don't. I keep looking at laptops but I rarely buy them.

user228700

But when you do, why do you..?

I see a laptop and think "ooh that would be nice" but sanity prevails and I don't buy it.

...wait, after the canonical quantisation in QFT, thus every observable became operator valued, what plays the analogous role of the wavefunction (or more generally, the quantum state) in QFT?

I only buy laptops if I have a use for them. I currently have four laptops of different types, and all of them get used regularly.

9:48 AM

that is, what are all these operators acting on?

user228700

@JohnRennie U bought the one I'm using right now off of Ebay, right..?

No, that one came from the company I work for.

user228700

Aaah, that explains a lot.

I did buy a similar laptop on ebay, which was just as well because it got us past the Indian customs :-)

user228700

:-) Yes, and that one also had a scratch on the screen?

9:50 AM

No. that one had no screen at all.

And no hard disk and no battery as I recall.

It is still in my pile of broken laptops waiting for me to get around to fixing it.

o wait nvm, we are using the heisenberg picture

user228700

@JohnRennie Oh, I see.

This one looks nice :-)

ebay.co.uk/itm/…

Expensive though ...

user228700

@JohnRennie That certainly explains a lot :-)

user228700

@JohnRennie Weren't u willing to pay about £200 for the other one?

9:52 AM

@Kaumudi.H yes, though it eventually sold for £250.

user228700

Oh, wow, that's crazy.

But this latest one is a much nicer laptop. I suspect it will sell for about £400.

user228700

Holy crap, yeah, that's expensive, I guess.

And I don't want a new laptop that much :-)

I'm vaguely looking for a laptop with a 17" screen to use when workign away from home (for comparison yours has a 14" screen)

but if I do buy one I will replace one of my current laptops i.e. I will sell a laptop or more likely give one away.

user228700

Oh, I see. Nice :-)

9:55 AM

A brand new one would be £600, which is a lot of money. That's why I'm keeping an eye open on ebay for a used one.

Q: What is the fundamental probabilistic interpretation of Quantum Fields?

10

In quantum mechanics, particles are described by wave functions, which describe probability amplitudes. In quantum field theory, particles are described by excitations of quantum fields. What is the analog of the quantum mechanical wave function? Is it a spectrum of field configurations (in analo...

quantum-mechanics quantum-field-theory probability born-rule

user228700

@JohnRennie Right, OK. Now I have a much better picture of the situation :-)

user228700

Oh God, I need to do something about this chapter...I feel like it's killing me, piece by piece. You were right, this chapter is fully of uninteresting silly problems.

> I don't like electrostatics. No. No. NO.

This proves you are a normal, sane, human being :-)

user228700

:-P I guess. It's totally boring and useless. Seriously, c'mon, for how much longer should I keep deriving stuff?! >.<

9:58 AM

If you find you've hit a block I would jump on to a more interesting chapter. Otherwise you are not using your time efficiently.

Or do what I do and go buy a laptop. Would you like another laptop?

user228700

@JohnRennie x'D Definitely not. This one's perfect <3

Every home should have at least four laptops :-)

user228700

--John HS (?) Rennie, 2017

??

Oh, attributing a quote

user228700

Yeah, that :-P

10:00 AM

We could talk about food ...

The good thing about food is that, unlike laptops, you always need more :-)

user228700

@JohnRennie :-) Yeah. Hey, quick question, would u prefer if, somehow, we got all the energy we need in a pill of some sort?

user228700

i.e: Do u want to savor the food/save up on all the time we spend eating?

Like most westerners I eat mainly for enjoyment. That is, the days when it was a struggle to get enough food to survive are centuries in the past.

user228700

:-) Right, OK.

10:03 AM

So no, I don't want to get all my nutrition from a pill. Though who knows, I might make an exception for the Hajmola :-)

Ok, so for the klein gordon equation, the hamiltonian can be decomposed into an integral of all the momentum vectors within the interval. Hmm I guess that's why QFT like to think about creation and annihilation operators.

But perhaps it might get more complicated as we move on to more advanced sections...

user228700

:-P I'm starting to get really worried if u'll throw up or something after eating it and then you will hate me for the rest of ur whole life.

are we in some sense... diagonalising the hamiltonian using this continuum basis of momentum wavevectors...?

@Kaumudi.H I'm looking forward to it. There are lots of posts on the web about westerners trying Hajmola and finding it disgusting, but my tastes are pretty wide. I grew up eating Indian, Chinese, Mediterranean and probably lots of other cuisines that I've forgotten.

There are very, very few foods I don't like. Strangely one of them is mustard, which is a traditional English condiment.

And tripe.

Tripe is one of the most disgusting foods known to man. Also traditionally English.

user228700

10:09 AM

> "Tripe is a type of edible lining from the stomachs of various farm animals."

user228700

WHYYY?!

@Kaumudi.H Exactly!

It's the inside of a cow's guts. Ugh.

Some eat the tongue

@Pissedofflayman Tongue is good!

user228700

@JohnRennie Gosh. Why is that a thing? Siriusly? (Yeah, I've replaced the word "Seriously" with "Siriusly" :-P )

10:10 AM

It's traditionally cooked as a pressed meat and it's very tasty. That's because it's pure muscle!

user228700

.__. This is getting weird, now.

Shifting the baseline works, I agree (because we never observe the absolute energy of the ground state anyway). But on closer look, I am wondering, are their really that many ks we need to integrate. Even if there are continuum many of them, what reason do we believe the integration domain cannot be bound like a line interval?
The look at that integral just screams like we might be able to treat E(k) as a density, which means it should be able to be normalised to some value depending on the region of integration, but that is only valid if for each component of k, it is not in the whole comp…

If you go back a hundred years getting enough food to live was a big deal. When an animal was slaughtered people would eat every last bit of it.

True

user228700

@JohnRennie Yeah, I guess that's true.

10:12 AM

My mother is 84 and she's probably from the last generation who had to eat every bit of the animal there is, so she is used to it. I have seen her eat pig's feet. Literally take a pigs foot, boil it, then eat it.

Not to mention remembering where we hid the food helped develop our brain.

user228700

@JohnRennie What? No. U're kidding, right? (About she belonging to that last generation and all)

The second world war was probably the turning point. My mum was born before the war and it was only after the war that life really started to improve for the average citizen.

user228700

Oh, wow, I see...

It's easy to take our modern way of life for granted, and forget that it wasn't always this way ...

Personally I can't understand how people survived without laptops :-)

user228700

10:17 AM

@JohnRennie Yeah, that's true. I just didn't think that...yeah, you're right.

user228700

Say, for how much longer will u be around..?

Another couple of hours or so.

Ok, that makes sense. The modes of the quanutm fields dictate the eignestates

user228700

@JohnRennie OK. I should probably do some physics but uuuugh >.<

10:20 AM

OK. I'll go make a coffee and read my mail. Ping me if you want to talk about (shudder) electrostatics :-)

user228700

Alright, never mind. I'm going to get some other stuff done real quick and I guess I'll have to not sleep tonight. Sigh. I'll see u later today, I guess. Bye :-)

Now I am wondering, what if we have two relativistics quantum systems with continuum many of degrees of freedom, which ground state should we take as the baseline for normalisation, or should we merge the ground states together into an effective ground state, and then renormalise the system using that...?

I think this is quite important cause we are talking about the indeterminate $\infty \pm \infty$ here in the expression, which can be potentially anything depending on the nature of the system

@Secret How do you post such long messages? Doesn't it exceed the word limit ?

linebreak screwed up formatting

@Secret What ?

I'm talking about word limit

10:27 AM

alternately, I just post one message immediately after another

Linebreaks screw up formatting, the text is interpreted as a quote and word limit don't apply to quotes

@Secret Oh I see. Thanks

Despite that, I have tried to my best to be concise, contrast my messages in these past 2 years to 3-4 years ago when I first joined

@Secret How do you put a line break without using the enter key ?

shift + enter

It only works on pc

Now I am wondering, what if we have two relativistics quantum systems with continuum many of degrees of freedom, which ground state should we take as the baseline for normalisation, or should we merge the ground states together into an effective ground state, and then renormalise the system using that...?

Line break

Wohoo

It works

:)

10:30 AM

my messages are also long for another reason: Because I post way too frequently

Hmm... a quantum field seemed like a superposition of continuum many configurations, and a general quantum state depends on part of this configuration while the eigenstate depends on only one or a few of them: the modes of the field

and if such modes obey dispersion relations, we then call these particles...?

10:58 AM

Let's see...:
(NB D is the dimension of the state space (thus we are not just talking about position space here)

1. Classical particle in 1D: A point like object governed by a time evolution (equation of motion) and symmetries (conservation laws) and has one degrees of freedom
2. Classical particles in nD: similar to 1 but has n degrees of freedom
3. Classical system of particles in 1D: N point like objects in a configuration governed by a time evolution and symmetries with 1 degrees of freedom each.

Ramanujan

11:20 AM

@Secret how to do on mobile?

you cannot

Ramanujan

:( I'm posting feature request

Help

11:42 AM

@Kaumudi.H you tagged wrong person (to me)