The h Bar - 2016-09-10 (page 2 of 3)

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2:00 PM

I can live fine without physics :)

@BalarkaSen There wasn't a video game discussion in quite a while :P

@BalarkaSen You must be platonist without realising it.

@SpaceOtter : good man. I have to say I don't much care. Not unless people elevate mathematical abstraction above hard scientific evidence and start suggesting the latter is not necessary. I wasn't too happy about Sean Carroll suggesting the scientific method was passé. See what Woit said.

@ACuriousMind Yes, I didn't see any recently either.

@SpaceOtter I have to admit I never remember what all the "ism" and "ist" mean.

That notion is passé!! It was given up by the scientific community not long after the middle ages!

2:05 PM

@BalarkaSen Let's see...do you believe math is discovered or invented? If the former, you're likely some form of platonist (it's common among mathematicians).

Which notion?

@ACuriousMind Oh, yeah, in a sense discovered.

We gave it up for prepositional logic!

@Timetraveler in general you don't merge the two theories. You discover that both theories are approximations of a (usually more complicated) third theory. So for example electricity and magnetism are both special cases of electromagnetism.

@SpaceOtter What is "it" in that sentence?

The notion that we do not need scientific evidence to make conclusions. That reason is enough and that if an argument is sound all it's conclusions must therefore be sound.

The teachings of Aristotle!

That's how old it is

2:07 PM

...and who was defending that notion?

I have no idea why you're talking about that

Apparently "Woit" and Sean Carroll

Why is "Woit" in scare quotes? Peter Woit is as real a person as Sean Carroll

It actually started by discussing wether maths was a science. Then it was brought up that some ppl are under the notion that the scientific method is "old hat"

@JohnDuffield What he said seems perfectly logical. You can't claim your theory is testable if there is no chance of failure

Ah, nevermind, I see that you were "discussing" with JD. I want no part of that.

@BalarkaSen Thought so, it's pretty rare for mathematicians to not at least in some sense believe that ;)

@SpaceOtter : this is the issue with string theory. It isn't testable so there's no chance of failure. But people have realised that it isn't science.

2:15 PM

Unsurprisingly.

ACM, well it was hardly fair to call it an argument or debate without another side represented.

@ACuriousMind Hello

@0celo7 heyhey

@ACuriousMind : why not discuss it with JD?

Clearly ACM is intimidated by you

2:18 PM

Guess it's time for 0celo7-conversations, which will invariably be wiping out metaphysics.

@JohnDuffield Scientific method can only strengthen our confidence in a theory. So string theorists should be free to find evidence that their theory can make reasonable predictions

@BalarkaSen Are you saying this is like some weird hbar variant of rock-paper-scissors? 0celo7-metaphysics-videogames?

Of course.

@0celo7 : and JR too. Such is my burden.

I think it's fair to say that almost everyone is intimidated by ACM, or rather, his ability to rip apart the tiniest flaw in someone's line of reasoning.

2:20 PM

user image

What?

lol

@ACuriousMind clicky

user116211

@0celo7 your cat?

Awww, Einstein!

@MAFIA36790 I think so

user116211

@0celo7 oh yeh, Einstein ;)

2:23 PM

24 mins ago, by Balarka Sen

Most of the discussions here are either metaphysics/metamathematics, philosophical, about video games, or 0celo7-conversations.

And ocassioanally, vzn and I dumping updates to physics and other fields

@SpaceOtter : when somebody comes up with a new hypothesis, we generally "cut it some slack". If there's no evidence for it, you don't dismiss it out of hand. You look for the evidence. If you find some, you develop it into a theory, make predictions, then find more evidence to match those predictions, and so on. But with string theory, it never got past first base. It started in the late sixties, see Wikipedia.

That's nearly fifty years ago. Now patience has run out.

It's uncertain whether it's 0celo7's cat or Schroedingers'. Does that make it Schroedinger's?

@ACuriousMind Suppose I have coordinate vector fields $\partial_i$ in some neighborhood of a point $p$. Are these automatically bounded on the neighborhood in any metric?

I'm thinking they have to be

I don't see any way the norms could blow up

If they do, just pick a smaller neighborhood

@SpaceOtter : he can't do that with me.

Norm is a continuous function...

2:26 PM

@BalarkaSen Correct, so?

Well, if the norm itself blows up towards the edge of the neighbourhood because you picked the entire manifold as the neighbourhood it might happen, no?

@BalarkaSen I think we might have discovered some, and then invented others based on our discovery. Hopefully we will be able to meet extraterrestials soon in our lifetime, because they will surely have something very different from our minds that we can learn from (e.g. maybe their mathematics are not subjected to the typical wiring of our human thought process)

But I think you'Re right that one can always pick a smaller neighbourhood on which these are bounded

Jd, So you're suggesting we give up string theory?

@ACuriousMind Yeah, perhaps.

2:27 PM

@BalarkaSen : I saw vector field.

user image

Oh god

The fact that the phenomenon we have seen in the real world can be classified so easily into patterns by our minds suggest our universe do somehow have a underlying mathematical structure of sort, otherwise, even with our tendency to think in patterns, it might not be always easy for us to sumarise them in nice equations at all

@ACuriousMind Suppose $x^i$ are normal coordinates about $p$. Then Petersen says continuity of $d\exp_p$ shows $|\partial_i|$ are bounded near $p$.

@0celo7 For any continuous function, and a point $p$, you can choose an nbhd $U$ where it's bounded above by an arbitrarily small constant.

I think that's a general feature of coordinate vector fields, not normal coordinates.

2:29 PM

@0celo7 I would agree

@BalarkaSen Right.

@SpaceOtter : yes. Or should I say Peter Woit is.

[Musings] Actually, speaking about extraterrestials, suppose we do managed to contact with them ans suppose they are not the invasive type. How can we ensure they will nto misinterpret our attempt to communicate as hostility given that both parties have no idea how the language system of each other worked?

@ACuriousMind Do you still have Secret blocked?

@Secret One can easily turn that argument on its head: Our minds are evolved to live in this world, so it's not surprising that they see "patterns" in it. In fact, we tend to see patterns even where there are none (give random data to people and they'll tell you about all sorts to patterns if you tell them to find some)

@0celo7 see above

2:32 PM

How far above?

Like, a message.

@0celo7 I replied to him directly above "see above"

Oh.

@Secret : it is what it is. Just because we try to describe it with mathematics doesn't mean it has an underlying mathematical structure. It doesn't mean it's made out of mathematics either: "I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure".

@ACuriousMind Li's geometric analysis contains "geodesic ball" 50 times <3

2:34 PM

Acurioismind, I agree, Speaking about that, even in some AI research I do see many times that the AI saw a leopard in otherwise random number generated black and white pixels (in an issue of newscientist.

Johnduffield: Recently I have been reading a couple of PSE and PhiloSE questions regarding MUH. While I don't think our universe is necessary a mathematical structure itself, based on what others discussed about the issue, whatever that non mathematical thing is currently beyond my comprehension. I might be able to comprehend that once my spirituality knowledge is good enough

@0celo7 That's...nice...

Is my new avatar not showing up correctly for anyone else?

0celo7: Avatar->Some kind of god like being

user image

@0celo7 It looks like your profile picture. If you're seeing something different, caching is to blame

@0celo7 That's...odd

2:39 PM

See above.

I saw the same gray cutoff

@Secret I blame Kanye.

@Secret : it's space. Spirituality won't help you with that.

What do I do

2

A: How do we prove or disprove that a particle has no internal structure?

The electron has a magnetic dipole moment and an intrinsic spin. Both phenomenon need an extend and a structure and hence the electron has to have an internal structure. That until know we haven't found this structure has to do with our capabilities to build the right instrument.

Jeez

2:44 PM

Aaaand anna v gets the 300-pont bounty.

@JohnRennie Why did you answer that question instead of one of the older duplicates Qmechanic linked?

@JohnDuffield Some discussions here. Also worth to type "supernatural" in the search bar for more info

Or, rather: How do you think this question is any different from the "How do we know the electron is pointlike?"/"Do electrons have shape?" questions?

@Secret : I think it's tosh.

@JohnRennie More worryingly, how did that get 3 upvotes? The answer is blatantly false.

2:49 PM

@0celo7 Buddha like pose when I click on it but looks half grey in thumbnail.

damn

how do I fix it

@JohnDuffield Who said "I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure" ?

@0celo7 Since it looks okay to me the problem is likely not one you can fix

lol 0celo7 is confus

Get a new avatar.

@BalarkaSen I did

user116211

2:52 PM

@0celo7 Now, it's good.

prntscr.com/cgehzx @0celo7

It's good on this end now.

Second downvote ever!

Oh it just fixed itself it seems

I hope my comment is making sense

> The two dimensional hilbert space that is needed to describe spin does not require some kind of spatial extent to be there. It is fine for something with no internal structure to have a state space of many dimensions

2:53 PM

Huh

Your avatar is fine now

yes, your avatar is fine for me now also

@SpaceOtter mod abuse, also known as "refresh profile from parent site" button

@Loong Abuse!

@0celo7 sorry

2:54 PM

but thanks

@Loong Huh? 0.o

@SpaceOtter : Max Tegmark. He talks about the multiverse. He's involved with the Templeton Foundation. He was also on TV saying a black hole's gravitational field is like a waterfall. This is a badly wrong analogy. I am not a fan.

0

Q: Can the Einstein Field Equations be written as Functional Equations?

I'm interested in describing physical systems with functional equations as opposed to differential equations. In an earlier question I gave an example - the Simple Harmonic Oscillator can be described by the functional equation: $$f(n) = kf(n-1) - f(n-2)$$ where n=2,3,4,5,.. and k is a constant...

general-relativity differential-equations

This guy likes to phrase things in terms of functional equations

Well that statement is essentially platonism in it's purest. @JohnDuffield

@Secret : if there's angular momentum, there has to be a spatial extent.

2:59 PM

@ACuriousMind I can't remember if Qmechanic posted the comment while I was writing my answer or after I posted the answer, but either way I didn't see it until after I had answered.

@JohnDuffield No, you are thinking too classically, the only thing that spin operator ever had to do with space is the orientation in xyz, as seen in the spin operator $\sigma_n=\sigma \cdot \vec{n}$, but not the size of it. IT could very well be a point like thing

@ACuriousMind Looking for patterns is the best thing you can do if you have to deal with a system with unknown behavior.

@Secret : no, it can't be pointlike. We have hard scientific evidence that it isn't pointlike, and no scientific evidence that it is.

@SpaceOtter : I'm not sure I know what you mean otter. All I can thing of at this juncture is abstract things are abstract.

Plato believed that we were in an abstract world that was an imperfect reprisentation of a pure and higher form

@SpaceOtter : he was a Greek philosopher. They weren't too keen on the scientific method. I am.

3:05 PM

Can you see how arguing that the physical world is merely an abstract form of a perfect mathematical form is so close to platonism or "neoplatonism"?

I wasn't saying he was right. I'm just saying the notion is old and platonistic. You said you didn't understand what I meant.

I think the belief itself is fine even if I don't share it, I only have problems when they suggest that physics is unnecessary since we could come to perfect reasoning about their hypothetical universe.

@SpaceOtter : OK fair enough.

Why are we even talking about this??

(To other guys who may be reading: I have just reached the halfway point of susskind's classical mechanics, hence the lagrangian formalism. Expect waves of classical mech question to come soon)

I say, it would be very interesting if we could actually make conclusions based on reasoning alone. Sigh. As they say, faith is the path of least resistance.

Petersen, you are literally Satan

3:13 PM

@SpaceOtter : we just wandered into it. Let's not talk about it any more. Let's talk physics instead.

He writes $A=B$

then says, so see this, note that $B'=A'$

so here I am trying to figure out why $A$ and $B'$ are equivalent

wtf?

What objects are A B A' B'?

$A=g(d\exp \partial_r,d\exp_p v), B=g_p(\partial_r,v), A'=\frac{1}{r}\delta_{ij}x^iv^j,B'=\frac{1}{r}g_{ij}x^ir^j$

it's obvious in hindsight

3:40 PM

[Worldbuilding musings] Some long time in the distant future, I need to build a universe with a very weird type of group structure such that it allows spin $\frac{1}{3}$ particles. Why? I have no idea, but I do have a preference for things to come in trios. Possibly because 3 is the smallest number needed to prevent people to ascribe the concept of dualism

(Reality check) Our 3+1 spacetime is governed by the poncaire' group and that does not allow anything other than half integer and integer spins (to get anyons you need to go down to 1+1 dimensions)

Talk amongst yourselves for a bit. I'll have my mouth full.

user image

I don't get spins.

4 mcmuffins? I am already full with one

McMuffins???

Those are home made cheeseburgers!

Though admittedly I didn't make the onion rings myself.

oops, but they do look like mc sausage muffins

The McMuffin is a family of breakfast sandwiches in various sizes and configurations, sold by the fast-food restaurant chain McDonald's. The Egg McMuffin is the signature breakfast sandwich. It was invented by Herb Peterson and brought into stores in 1972. == Product description == In the US and Canada the standard McMuffin consists of a slice of Canadian bacon, a griddle-fried egg, and a slice of American cheese on a toasted and buttered English muffin. The round shape of the egg is made by cooking it in a white plastic ring surrounded by an outer metal structure. === Variants === McM...

3:43 PM

I guess muffins all look fairly similar :-)

@Secret That doesn't make much sense since the assignment of "half-integer" and "integer" to spins is arbitrary to begin with. If you declare $\hbar' = \frac{2}{3}\hbar$ and meansure spin in unit of $\hbar'$, then you get "1/3-spins" without changing any physics.

@BalarkaSen It's just a number that labels an $\mathrm{SU}(2)$-representation. ;)

I only go to McDonalds when I want to ask the mathematicians if they're got a proper job yet.

@ACuriousMind SU(2)-representation of what?

@JohnRennie For some reason I take that as a compliment.

I know I shouldn't.

(Technically I am not a mathematician though)

@ACuriousMind wait I thought based on what I read in the feymann lecturers, because you can only get a phase change of 1 or -1 when you brought two identical particles to interfere, and then by the spin statistics theorem you get half integers and integers as a result of the possible spins. I never realise that the way they define them as integers or half integers are arbitrary

@BalarkaSen What do you mean "of what"? It's a group representation of $\mathrm{SU}(2)$ upon the Hilbert space of states.

3:48 PM

I meant "in what".

typo: lecture, not lecturers

@ACuriousMind So, why are they interesting?

typo 2: No I mean spin statistics theorem say that bosons are integers while fermions are half integer spins

@Secret The important thing is that there are two distinct "kinds" of spin. Whether you call them "half-integer" and "integer" or "even" and "odd" or whatever else doesn't matter.

@BalarkaSen Because we must know how physics behaves under the rotation group SO(3) - since rotations are a classical symmetry of many theories. Wigner's theorem says symmetries are given by projective representations in the quantum theory, and the projective representations of SO(3) are equivalent to linear unitary representations of SU(2), its universal cover.

ok I see, in that case, my worldbuilding musing should be rephrased that I am trying to introduce a 3rd type of spin by building a universe not based on SU(2) (not that it is important nor a question anyway)

3:51 PM

@BalarkaSen :-)

Here, have this gratuitous insult. It's free!

So for any given quantum state, we must know in which representation of SU(2) it transforms. Most interestingly, it turns out that point-like particles like the electron transform in non-trivial representations (if we want to match experimental results like Stern-Gerlach)!

@ACuriousMind Hmm.

@Secret negative temperature is relatively simple.

@DanielSank know, it's because the energy levels become less degenerate as you increase the energy of the system (as oppose to being more degeenrate in a boltzmann fashion), but then what is temperature physically characterising when you consider both inverted population systems and ordinary systems together?

Or phrase it in another way ,what single sentence description will capture the physical meaning of temperature such that it can describe both the positive temperature and negative temperature systems?

1/T = dS/dE

^ That

4:02 PM

@ACuriousMind So, what is the spin of such a representation/action on the Hilbert space?

@DanielSank So it is really just a change of energy wrt change in accessible microstates in a process, and not something deeper or (insert suitable word)?

Yes

18

Q: Is the Boltzmann constant really that important?

I read a book in which one chapter gave a speech about the fundamental constants of the Universe, and I remember it stated this: If the mass of an electron, the Planck constant, the speed of light, or the mass of a proton were even just slightly different (smaller or bigger) than what they ac...

thermodynamics physical-constants

I explain it there.

Spin is a real rotation. The Einstein-de Haas effect demonstrates that "spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics."

temperature arises as we maximise entropy under fixed energy..., ok

@BalarkaSen Do not listen to JD.

4:06 PM

I think you misspelled

Indeed.

Stupid mobile interface

Although JR cost me $30 once, so be weary of that interaction too.

The electron magnetic moment is there because "From classical electrodynamics, a rotating electrically charged body creates a magnetic dipole with magnetic poles of equal magnitude but opposite polarity. This analogy holds as an electron indeed behaves like a tiny bar magnet." Only the electron isn't a rotating ball of charge. It has a wave nature, as evidence by electron diffraction.

Who flagged Secret's last post? What on Earth was that for?

4:07 PM

Or is it wary?

Accidentally flagged it.

I can't English.

@0celo7 weary and wary :-)

Frantically tried to un-flag.

I am wearied by interactions with @0celo7, for sure.

4:08 PM

@BalarkaSen That's not very nice.

Though I think you would be wise to be wary of interactions with 0celo7

@JohnRennie wtf have I done to you

::face palm::

@0celo7 You tried to tell me about balls and my brain exploded

@BalarkaSen : the evidence is there. Some people would prefer you to ignore it.

@JohnRennie I can't help it that my balls are so interesting

4:10 PM

To danielsank: The following post wil be relevant to the next queston I am going to ask:

@JohnRennie I edited and it's perhaps less unnice.

1

Q: Can entropy be regarded as energy dispersal?

In several answers here the claim has been made that thermodynamic entropy can be regarded as energy dispersion. See, in particular here, and here and here. This is apparently the pet theory of a chemistry professor, Frank Lambert. Apparently (at least according to his Wikipedia page) this defini...

thermodynamics statistical-mechanics entropy

@DanielSank When a process result in a change in entropy, that is, a change in the number of accessible microstates, do the energy always end up distributed to these new microstate, hence in a sense an energy dispersal. Or can we increase a system's accessible microstate without energy being dispersed in the configuration space or in a sensne "diluted" over many microstates?

@0celo7 Oh God, I feel nauseous now and I've just eaten a big lunch ...

(I should mention that I am joking; although some version of it is of course true)

@Secret in equilibrium we usually assume each microstate is equally likely.

That assumption leads to a lot of experimentally verified predictions, so it seems like a good one even if it's an approximation.

4:14 PM

@DanielSank But is energy the only possible thing that will be diluted over the accessible microstates as the system explores them ergodically. That is, do entropy and energy must be tied together such that when one changes, so is the other, thus making "entropy as a measure of energy dispersal over accessible microstate" an accurate description of entropy?

@BalarkaSen It turns out that you can classify the finite-dimensional unitary representations of SU(2) by a single number $s$ (it has only one independent Casimir, whose eigenvalue on an irrep is $s(s+1)$). This single number is the "spin".

Right, I guessed. Is it tedious to define $s$?

@Secret no

At least, I don't think so.

@JohnRennie I don't get that

Nothing ever makes me feel sick/queasy

@BalarkaSen Not if you are familiar with a bit of representation theory, I guess it's a highest weight.

4:16 PM

But I don't know what you mean by a measure of energy dispersal.

@ACuriousMind My prof wants me to translate a German article, how much do I have to pay you to do it

@0celo7 Except antibiotics eaten while starving.

@BalarkaSen True

But I wasn't starving

@ACuriousMind What does "Dünnschliffen" mean?

Not the Google translate answer

I think it means "thin strips"

@DanielSank Like when you have two subsystems with $m_1$ accessible microstates and $m_2$ accessible microstates respectively, then when you brought them to thermal contact, you have a larger system with $m1m2$ accesisble microstates. The energy dispersal will mean that any energy that is

initially partitioned inside the subsystems now get dispersed through this combined system because it is more likely for the combined system to explore those microstates with less energy in it before putting them together

So in the PSE example of the two level system, the system with more degeneracy get an increase in energy while the less degeenrate system loses energy

thus in a sense the total energy get diluted over all the microstates

I then wonder whether energy is the only thing that end up being diluted over the microstates, or whether they can be another physical quality that can exhibit this also

@DanielSank That is, we knew that entropy is a measure of the number of accessible microstates (and this number is controlled by various things including the energy in the system). What makes the energy distribution in the system to change whenever it has extra microstates it can access to, why will energy want to move to these new microstates instead of just the system explore them without dragging energy along with it?

> it is more likely for the combined system to explore those microstates with less energy in it before putting them together

What?

4:30 PM

@BalarkaSen Classical $\vec{r} \times \vec{p}$ quantizes to integer units of $\hbar$. Spin quantizes to half-integer units of $\hbar$, so spin isn't $\vec{r} \times \vec{p}$. The evidence is there, but some people would prefer that you ignore it.

(elaborate what you just quoted above). The two level system in that PSE link, after brought into thermal contact and then separated again, energy end up in the more degenerate subsystem and energy is lost from the less degenerate system.

@dmckee What? The Einstein-de Haas effect clearly states that spin has the same nature as angular momentum. You're lost in the math.

Why there exists no microstates such that a non-energy type physical quantity of the system changed instead, thus preventing energy from moving to more denegerate subsystems?

@Secret Yes. That maximizes the total entropy.

@Secret It is always frustrating when a question starts with an incorrect statement.

@dmckee : half integer ħ spin is not evidence that intrinsic spin is not a real rotation.

4:35 PM

@JohnDuffield Care to explain that with real quantitative theory substantiated by experimental evidence?

4

@Secret do you know about chemical potential?

@DanielSank yes, it is tied to the concentration of particles in a systems, such as various chemical species, and it is $\frac{\partial G}{\partial n}=\mu$

@Secret Right. Chemical potential is the Lagrange multiplier associated with the constraint of fixed particle number.

yes

It's just like temperature is the Lagrange multiplier associated with the constraint of fixed energy.

So of course there is a quantity, other than energy, which dictates the equilibrium arrangement of a system.

@DanielSank : no. But I can show it to you. See Robert Gray’s web site.

4:39 PM

@dmckee Is the rotation of a point particle of the form $r\times p$?

What is $r$?

Or $p$...

ok

@JohnDuffield Yes, this is a somewhat well know way to illustrate spin.

Perhaps your statement about spin being a "real rotation" is a bit vague and I don't know what you mean.

@0celo7 These questions have no answers clear. How could they?

@dmckee What?

It's one of the thing the fans and practitioners of string theory point at when suggesting that we need a better theory.

4:47 PM

@dmckee So, you don't know if the electron is actually spinning?

But apparently fundamental particle do have angular momentum and that angular momentum takes on values forbidden to $\vec{r} \times \vec{p}$.

But that doesn't rule out the electron spinning?

@0celo7 I know that the electron's angular momentum has a value that is forbidden to a spinning ball. Or indeed to any other spinning shape.

@DanielSank : I meant what I said. There's a canard in physics, which goes back to Pauli in 1925. You can find it on an old Stern-Gerlach article: "Even if the electron radius were as large as 2.8 fm (the classical electron radius), its surface would have to be rotating at 2.3 × 10^11 m/s. The speed of rotation at the surface would be in excess of the speed of light, 2.998 × 10^8 m/s, and is thus impossible. Instead, the spin angular momentum is a purely quantum mechanical phenomenon”.

Q2. Suppose I have a system A placed in constant pressure and fixed number of particles with 3 degenerate states of energy $E1$ and system B under the same condition with 5 degenerate states of energy

$E2$. After A interact with B and then separated again, A now has 4 degenerate states while B still has 5. Is it possible when A explores the 4 degenerate states (thus this technically speaking is an increase in entropy because previously A has only 3 states it can explore), no energy ends up being partitioned into the 4th state thus the energy distribution in A remains thesame?

4:49 PM

@dmckee How so?

You just said my question had no clear answer.

Because any angular momentum that can be expressed in the classical way ($\vec{r} \times \vec{p}$ will have a quantization on integer values of $\hbar$.

I know that, but if the electron is pointlike then the angular momentum is not of the form $r\times p$, is it?

What is $r$?

@0celo7 Sorry. I meant the questions "What is r?" and What is p?.

@DanielSank : See Wikipedia: "If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast". It's a non-sequitur. An electron doesn't rotate like a planet. It's a spin ½ particle.

That is, can A explore the 4 degenerate states without actually occupying the 4th state (thus result in the 4th state to contribute no energy to A despite it has the same energy as the other 3 if being occupied)?

4:52 PM

@JohnDuffield I think you're arguing both sides of the issue.

@0celo7 That's the whole point. An electron's angular momentum isn't $\vec{r} \times \vec{p}$.

Is the electron a spinning top or not?

@dmckee I agree, but maybe it's still rotating.

@0celo7 It "has spin". That doesn't mean it is a rotating ball.

@dmckee How do we know that?

Using the word "spinning" opens avenues for misunderstanding.

4:53 PM

@0celo7 : no I'm not. I'm saying electron spin is a real rotation. And that the electron is not a point particle. Nor is it a rotating ball. It doesn't rotate like a planet.

@JohnDuffield Ok, what is a "real rotation" if not a "ball rotation"?

It's a wave going around and around. Like this.

user image

nvm the previous phrasing of Q2 is too confusing let me rephrase it again

@JohnDuffield What?

Like this:

user image

The electron doesn't have an electric field. It doesn't have a magnetic field. It has an electromagnetic field.

user image

Time for tea!

Bye.

4:57 PM

...

It amuses me to note that John's two pictures here contradict one another. The equitorial Poynting vector in the line figure is purely polar, but his animation shows it with a axial component.

@dmckee Q2 (revised) Suppose I have a system A which is a particle characterized by two quantities (energy,something else) with 5 degenerate states. The 5 degenerate states have properties labelled as follows (E,1), (E,1), (E,1), (E,1), (E,2).

Is it possible for A to explore all 5 degenerate states, but never actually occupied the (E,2) state, thus result in it to have no energy contribution to A?

@JohnDuffield what kind of tea do you drink :P

@Secret Statistical physics is not my strong suit, but don't the notion of "contribute to the [partition function|expectation value]" and "explore the state" go together?

o crap, yes you are right...

nvm then

5:11 PM

Re: how do I know the electron is not rotating. If it did, wouldn't it radiate electromagnetic waves?

Rotating as in actually spinning in the classical sense.

I have no idea how that works, so I'm just guessing.

@JohnRennie You can add me to the list of people who reveled in their doctoral studies, but I also faced some nasty life challenges and intense pressures during that time.

@dmckee Why does @JohnDuffield keep reminding everyone that the electromagnetic field is the electromagnetic field? Does he think we don't know that?

So I always suggest that people think carefully about what they are giving up and how badly they want it before applying to grad school. Tell them to talk to some working scientists and engineers outside of academia before locking on to "a tenure track position at a R1".

Also, I am a bit concerned about the banana.

The "Peanut Butter Jelly Time" banana is one of my favorite things.

@DanielSank Introductory materials treat them as separate in the static limit (a good approximation for many purposes), and if you weren't paying attention I suppose you could miss the importance of the coupling the time it is introduced. Maybe he thinks it's deep.

5:25 PM

@dmckee But... ok.

Why remind us of that fact when we all know it?

@JohnDuffield Nobody here thinks spin has anything to do with the electron actually spinning like a ball.

@JohnRennie That's not a cliche. A lot of people are miserable during their PhD years because the system invites prolonged abuse without recourse.

(Super weird question that I am not sure if it make sense) Danielsank, and dmckee, is it possible to have a state which has energy expectaton value of zero despite it has nonzero energy, thus result in a weird scenario that even if it is being occupied as the system explore the state, it end up contribute nothing to the system as if the state never exists at least in the context of energy (yet can still be experimentally detected because its e.g. volume, pressure etc. can still be detected)?

@DanielSank It may be wrapped up with his fascination with that spiral visualization he was posting all the time for a while.

Though I've never understood why he thought it was a good idea to add different components of a rank-2 tensor and hope that the sum meant something.

@DanielSank Prolonged abuse?

All the grad students I've known have been pretty happy. I'm at an R1 but not a super competitive school.

5:52 PM

@yuggib Do states with 1) zero energy eigenvalues and/or 2) zero energy expectation value exists in any known physical systems? If they do, does it mean if I have a system with many states, putting a particle on any of these states will not contribute to the energy of the system?

@Secret of course there are states with zero energy, and they're usually taken as the ground state of the system

also, there is a freedom in choosing the bottom energy of a theory

@JohnDuffield Not being a physicist, I am few to check your theories deeply, but if I would be one, I would.

The vacuum state in a field theory, for example, usually is an eigenvector with zero eigenvalue of the hamiltonian

but you cannot "add a particle in a vacuum state" because the vacuum state is interpreted as a state with no particles

I see

@0celo7 That's good.

Very happy to hear that.

5:58 PM

@yuggib If I have an energy level in a system which is positive (e.g. an excited state) is it guarenteed that for any possible eigenfunction that corresponds to this energy, the expectation value of energy is always positive definite thus never can equal to zero for this energy level?

the expectation value of the energy for an energy eigenvector is rather trivial...it is the eigenvalue corresponding to such eigenvector essentially by definition

ooops

if $H\psi=\lambda\psi$, then $\langle \psi, H\psi\rangle=\langle \psi,\lambda\psi\rangle=\lambda\langle\psi,\psi\rangle=\lambda$ since a state is normalized

if $\lambda>0$, then $\langle\psi,H\psi\rangle>0$

yup

@yuggib Combined with the knwoledge of this answer here, are all zero energy modes basically vacuum states?

19

Q: Zero modes ~ zero eigenvalue modes ~ zero energy modes?

There have been several Phys.SE questions on the topic of zero modes. Such as, e.g., zero-modes (What are zero modes?, Can massive fermions have zero modes?), majorana-zero-modes (Majorana zero mode in quantum field theory), path-integral-with-zero-energy-modes (Path integral with zero energy...

quantum-field-theory string-theory research-level topological-field-theory topological-order

6:16 PM

@0celo7 There was a professor at my grad school (a theorists, so I didn't work closely with him) who had a reputation for endless expecting new work of students.

He always had them sign as the first author, but the papers his students wrote were almost the only ones with his name on them.

@Secret not necessarily; it depeds from the model and type of interaction

@yuggib Got Evans for $60

Seems like a good deal

At one point things got bad enough that when he went on vacation to the old country the rest of a student's committee conveyned, examined her and signed off on her dissertation before he every got back.

@dmckee I don't know what you're saying here

The general feeling was that she should have been graduated a couple of years earlier.

6:19 PM

@dmckee What?

Who is she?

@0celo7 I'm saying that while he was still a fruitful source of ideas his students were doing all his work. And yeah, the committee examining a student without the advisor is exceptional.

They may have had to formally assign her a new advisor to get it done.

@0celo7 The student.

@dmckee Isn't that how experimental physics works?

@0celo7 That was theory.

@dmckee The edited apostrophe was crucial to understanding that sentence.

And even in experiment the professor is expected to pitch in more than starting ideas and funding.

Though we all know they don't have enough spare time to do a lot of heavy lifting, they are expected to keep their hand in.

6:23 PM

what are they supposed to do?

Contribute some analysis, sit some shifts, help on the design and construction of the bits their people are putting together because they've done it before. Take care of nasty administrative stuff like software release scheduling and management.

A couple of my bosses were master of short-cut analysis to demonstrate the possible feasibility of a real analysis. And to add insult to injury they'd do them on the plane on the way to some meeting.

I never get anything worthwhile done on planes.

My advisor read and understood the 50 page proof of triagulability of smooth manifolds on a plane...

user218912

@0celo7 do you remember any physics?

user218912

I have a question

@3075 Depends what kind of physics.

user218912

6:32 PM

GR

user218912

remember you said

user218912

Jun 10 at 21:31, by 0celo7

@3075 but what about in theories where there is no time translation invariance?

user218912

can you explain what this means again?

To use Noether's theorem, you need a time translation symmetry.

In general, there is no such symmetry in GR.

user218912

why?

6:34 PM

Because the metric is time-dependent.

@0celo7 not bad ;-)

user218912

oh okay.

user218912

thanks :D

@3075 The GR Hamiltonian is fucked up, and it will depend on time.

(or Lagrangian)

user218912

okay thanks I'll read up about this.

6:38 PM

@yuggib If $f:\Omega\subset\Bbb R^n\to \Bbb R$ is Lipschitz, what does it mean that $\Delta f\ge 0$ in the "sense of distributions"?

6:53 PM

0

Q: What is the Latex and MathJax, how can I write beautiful formulas in my posts?

I get regularly the feedback in comments to use Latex or MathJax. Also I would write beautiful formulas what I can do only on pen & paper. Where can I get info about these?

support mathjax tex community-wiki

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