The h Bar - 2020-10-18

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ZeroTheHero

00:13

@Archer Correlation is not useless: if there's no correlation between two "events" it's unlikely that one is the cause of the other. The other away around doesn't work though.

ZeroTheHero

00:33

Causation is actually really hard to prove. Just tell the tobacco company: not every smoker gets lung cancer, and not everyone getting lung cancer is a smoker. However by careful use of control groups one can eliminate alternative causes.

4 hours later…

Jack Rod

04:17

phys.org/news/…

energy spectrum of universe

2 hours later…

Sir Cumference

06:36

@ZeroTheHero that x axis bothers me

35000 > 45000 > 20000

3 hours later…

Slereah

09:26

The issue of proving causation is that the universe is never in the same state anyway

So how can you tell!

You don't know if the time, the color of the experimenter's shirt or whatever is happening in the nearby galaxy is influencing the experiment

1 hour later…

Jack Rod

10:44

@JohnRennie hi

John Rennie

@JackRod hi :-)

Jack Rod

What is the central force in physics?

John Rennie

A central force is a force that always points towards the same point in space.

For example consider the gravitational force from a sphere. This force always points towards the centre of the sphere, so it is a central force.

Jack Rod

OK what is the torque about this point

if I have a regular shape body

John Rennie

Do you mean something like a rectangular shaped body orbiting a point mass?

And you're asking if the central force can create a torque on the rectangular body?

Jack Rod

10:49

yes

can we expect any torque from it

John Rennie

The central force cannot exert a torque on the body i.e. the torque on the body due to the central force is zero.

The central force just produces a net force acting through the centre of mass of the orbiting body.

Jack Rod

ok that's where I have the confusion actually our friend asked what is a central force I said a force which act along the centre of the body

John Rennie

I can see the scope for confusion, because there are two "centres" - the centre of the planet and the centre of the orbiting body.

Gravity is a bit special because mass only comes with one sign i.e. all masses are positive.

It is possible for a central field to exert a torque. For example consider the field created by a point charge. This is a central field like the field created by a point mass.

But if you put an electric dipole in the field there will be a torque on the dipole.

Jack Rod

hmm!

JingleBells

11:05

@ACuriousMind It turns out I actually absorb more and I learn better from reading. I'm just lazy most of the time so I refer to videos (which quickly give me a vague idea of the topic). But when I sit down and I really focus on a book (article, or even Wikipedia) I grasp the concepts faster and more in-depth. So I agree with you - reading is better for learning because you set your own pace to learn at and unlike with videos, you dive deep into the topic.

I watch videos when I'm lazy, tired, and need a quick intuition/introduction to a topic. But when you need a deep understanding of something, it's better to get a book, sit down and focus. After 15 minutes you get into a state where you've lost track of time and you absorb the info like a sponge.

JingleBells

11:37

user image

ACuriousMind

12:01

how did you think a casino makes profit? :P

Emilio Pisanty

0

Q: Why do atoms oscillate at absolute zero?

I have heard that average kinetic energy of atoms is directly proportional to the absolute temperature . Then why don't atoms come to a stop at absolute zero(T=0k).

atomic-physics atoms cold-atoms

presumably a duplicate?

ACuriousMind

@EmilioPisanty physics.stackexchange.com/q/113490/50583?

Charlie

12:41

On a manifold there's no requirement that every element of the topology have at least one chart map right? The only requirement is that the charts provide an open cover for the manifold

This is mostly motivated by manifolds with curvature singularities, then again I'm pretty sure I've asked a related question before and the answer was more advanced than I could understand

ACuriousMind

@Charlie What do you mean by "every element of the topology"? Open sets? There's usually lots of open sets at aren't connected and hence don't have charts on them since they can't possibly be homeomorphic to $\mathbb{R}^n$.

Charlie

Yeah I meant open sets, that makes sense too ty, I guess an example would be non-simply connected Lie groups?

Uh actually I don't see why disconnected open sets can't be homeomorphic to $\Bbb R^n$, we can define disconnected open sets in $\Bbb R^n$ which means the charts can be continuous

ACuriousMind

@Charlie No, an example would already be just two disjoint open balls in $\mathbb{R}^n$

Charlie

What property of the homeomorphism fails on them?

ACuriousMind

$\mathbb{R}^n$ is a manifold, and the union of an open ball at $p_1$ and an open ball at $p_2$ is an open set that's disconnected if we choose the radius small enough

@Charlie homeomorphisms preserve connectedness properties

Charlie

12:56

Does it not count if the connectedness property to be preserved is non-connectedness?

ACuriousMind

what's your definition of a chart?

my definition says it goes between some open set on the manifold and some open ball in $\mathbb{R}^n$

Charlie

Just a homeomorphism to $\Bbb R^n$

ACuriousMind

@Charlie right, and $\mathbb{R}^n$ is connected

Charlie

Is the union of open balls in Rn not again open?

ACuriousMind

so you can't get a chart from some disconnected set to $\mathbb{R}^n$.

Charlie

12:58

oh my god the chart maps are surjective

ACuriousMind

@Charlie sure it is

@Charlie they're even bijective!

that's what being a homeomorphism means

Charlie

that literally hadn't even occurred to me

oh man that actually changes a lot

user image

i'm so used to this kind of image

it corrupted me

because it doesn't look surjective so it never even crossed my mind

well, ty :P

ACuriousMind

it's surjective onto the subsets of $\mathbb{R}^n$ :P

Charlie

oh wait I wasn't going crazy

ACuriousMind

some people define a chart to be to some open ball in $\mathbb{R}^n$ instead of the whole (every open ball is homeomorphic to $\mathbb{R}^n$ so this doesn't really matter)

Charlie

13:00

ughhh

oh I actually didn't know that last fact

I assume the reasoning is then since isomorphisms are transitive if $U\subseteq \mathcal M$ is homeomorphic to some subset of $\Bbb R^n$ then it must be homemorphic to all of $\Bbb R^n$ and therefore has to be connected since $\Bbb R^n$ is

ACuriousMind

it's simple to see - choose polar coordinates centered at the center of the ball, the ball has some radius $R$, the map $(r,\phi,\theta)\mapsto (r/(R-r),\phi,\theta)$ is the homeomorphism

@Charlie not all subsets of $\mathbb{R}^n$ are homomorphic to $\mathbb{R}^n$, this is specific to the open ball

Charlie

-oh

ACuriousMind

a closed ball is also a subset of $\mathbb{R}^n$ but not homeomorphic to $\mathbb{R}^n$ - the closed ball is compact, $\mathbb{R}^n$ is not

Charlie

I don't suppose by some miracle the codomain of chart maps is always an open ball is it?

oh but all open subsets of $\Bbb R^n$ are homeomorphic to the open ball?

ACuriousMind

@Charlie Why "miracle"? You make that part of the definition

@Charlie no, I already gave the disjoint union of two open balls as an example :P

Charlie

13:14

Ok everything makes sense now so far, the only strange part is that disconnected open sets on the manifold can still be validly homeomorphic to disjoint open balls in $\Bbb R^n$, but I guess it's fine if we exclude them as part of the definition of the charts

Ratman

I thnk you should check that also other topological properties like connectedeness or simple connectedness are shared by the two sets, if at least one is not shared there can't be a homeomorphism

as a general approach, not to this particular case

Charlie

Yeah they're called topological invariants or something right?

I wasn't actually aware that connectedness and simple connectedness were distinct properties lol, it's been a while since I purposly read about topology

Ratman

yes exactly

shelton Benjamin

can i ask questions

Charlie

13:30

The rule is usually don't ask about asking, just go for it

shelton Benjamin

user image

if we give a explanation using concept of com then since the com is moving down so ball should also move down so it perform oscillatory moytion

but is there a explanation without concept of com

also why motion of com is oscillatory

@Charlie when i see such discussion i think its better to ask

Slereah

14:30

@Charlie It's not, but there always exists a chart of a manifold such that everything is homeomorphic to a ball

it is sometimes more convenient to use such a chart

it's easy enough to prove since every open set has open balls as a basis

Charlie

I don't understand that first message, when you say "everything is homeomorphic to a ball" what does "everything" mean? All open sets on M?

What I gathered from the discussion earlier was mostly that disconnected open sets in M don't have a chart map

I assume that even if there are open sets containing disconnected components of M we can still define a chart on each disconnected component separately

Slereah

I'm saying that, given a manifold $M$, there exists a collection of charts $\{ (U, \phi) \}$ such that, for every such $(U, \phi)$, $\phi(U)$ is a ball

Charlie

oh

bolbteppa

15:31

"A good way to approach the subject is the way Sophus Lie did himself. A Lie group is a group with continuous (or smooth) parameters. We convert the associativity of the group law into a differential equation, and study the integrability of that differential equation."

Ratman

15:52

It is kind of amazing what Lie did

In calculus, we learned about the Taylor or power series. Taylor said that if we gave him
all the derivatives of a function f (x) at x = 0 (say), he could construct the function. In
contrast, Lie said that, thanks to the multiplicative group structure, he only needs the first
derivative of the group element R(θ) near the identity.

a quote from Zee i really like

John Duffield

16:43

@bolbteppa : sorry, what paper?

bolbteppa

The Born-Infeld one you linked to

John Duffield

@bolbteppa : no, but I'd say they were saying spin is a real rotation. Hans Ohanian wrote a paper about that in 1984, see staff.fnwi.uva.nl/m.renzo/materials/WhatIsSpin.pdf

bolbteppa

It seems like they are saying a couple of things like that, it would be interesting to read someone's analysis of it

John Duffield

He referred to Frederik Belinfante's 1939 paper On the spin angular momentum of mesons.

@bolbteppa : what puzzles me is that Einstein worked with Leopold Infeld on the nature of particles, but didn't use anything from the Born-Infeld model. There was a peper they wrote together with another guy. Hang on, I'll dig it up...

The paper is The Gravitational Equations and the Problem of Motion

It's all about point-particles. I've tried to research Einstein's unification work but I haven't really gotten anywhere with it.

@AcuriousMind: what's your policy on referring to Sci-Hub?

bolbteppa

17:02

22

Q: What is the prevailing opinion in scientific community about Hans C. Ohanian's description of spin?

In the paper What is spin?, Am. J. Phys. 54 (1986) 500, by Hans C. Ohanian, spin is described as a circulating flow of energy in the wave-field of a particle. Is this the generally agreed upon explanation of intrinsic angular momentum or just a fringe theory? (A similar thread exists on Reddit,...

quantum-mechanics angular-momentum quantum-spin

Sir Cumference

when Euler lost his $i$ he couldn't $\mathbb{C}$ anymore

Azmuth

@Charlie lol

@SirCumference lmao!

John Duffield

@bolbteppa : I'd say Anna's answer gives the prevailing opinion. The electron is treated as a point-particle, even though the evidence of the Davisson-Germer experiment and the diffraction experiments by George Paget Thomson and Andrew Reid proved the wave nature of matter, which is why de Broglie got his Nobel prize.

I think it's worth reading about Larmor precession: en.wikipedia.org/wiki/Larmor_precession

bolbteppa

Well I still don't really know what's going on with this really, it certainly looks like a contradiction for every QM book to say spin has no classical analogue then to see classical EM having something they call spin

John Duffield

As far as I can tell Schrodinger plus others like de Broglie and Charles Galton Darwin proposed a realistic electron in the 1920s, but the Copenhagen guys who were their rivals promoted Yakov Frenkel’s point-particle electron. The Copenhagen guys "won".

Yakov Frenkel's paper is here: neo-classical-physics.info/uploads/3/4/3/6/34363841/…

bolbteppa

17:11

If you don't assume they are point particles, nothing makes sense, it breaks special relativity to try to model them as rigid bodies because a 'push' on one part takes time to propagate (because of relativity, it's instant to Newton) to the other parts so it simply can't be a rigid body, if they are not rigid bodies they are made of 'stuff' and there's no reason why you can't zoom in to find out what the stuff is. The only way to bypass this is string theory

John Duffield

I think it only makes sense if you don't model them as point particles. Read that Wikipedia article on Larmor precession. If you know about the gyroscopic precession of a boomerang, you can liken that to the circular motion of an electron in a uniform magnetic field.

bolbteppa

Belinfante–Rosenfeld stress–energy tensor

In mathematical physics, the Belinfante–Rosenfeld tensor is a modification of the energy–momentum tensor that is constructed from the canonical energy–momentum tensor and the spin current so as to be symmetric yet still conserved. In a classical or quantum local field theory, the generator of Lorentz transformations can be written as an integral M μ ν = ∫ d 3 x...

Azmuth

@bolbteppa Oh yeah. I totally forgot this one, thanks for reminding me :)

bolbteppa

So the question is, if the Belinfante tensor always has a 'spin' term, even for classical fields, why doesn't this immediately mean the whole concept of spin arising as a quantum concept in the representation theory is wrong

John Duffield

@bolbteppa : I learn something new every day. Thanks.

I don't know the answer to qyour question I'm afraid. But I do like this from Feynman: “Suppose we take the example of a point charge sitting near the center of a bar magnet, as shown in Fig. 27–6. Everything is at rest, so the energy is not changing with time. Also, E and B are quite static. But the Poynting vector says that there is a flow of energy, because there is an E × B that is not zero. If you look at the energy flow, you find that it just circulates around and around..."

I have to go I'm afraid. Time for a glass of vino with the Mrs.

JingleBells

18:08

You know how we boil water to turn it into steam so it rotates a turbine that produces electricity? Why don't we go to Mount Everest and boil the water there for free? :D

Faded Giant

🙄

JingleBells

😎

skillpatrol

🤔

JingleBells

18:27

Hmm, instead of covering a 100x100 meter area with solar panels, why don't have one really strong and heat resistive solar panel in the middle and one big lens on top of it?

skillpatrol

🙄

JingleBells

😎

2 hours later…

ACuriousMind

20:35

@JohnDuffield We prefer no direct links to copyright-violating material

Charlie

21:09

I can't imagine the answer being no :P

skillpatrol

thanks for your imaginative comment :P

but I don't think now is the time

2 hours later...

user image

4

:-)

Physics Meta

21:59

0

Q: How can I get the order of question in a search to be by date?

I frequently so a search with the following: [cosmology] answers:0 . I would like the questions ordered by the date they were asked with the most recent first. How can I make this happen?

feature-request

1 hour later…

peterh - Reinstate Monica

23:00

@skillpatrol Right, but in programming, you can fix the code before release. There is no way to fix a book if it is already printed.

peterh - Reinstate Monica

23:29

@ACuriousMind Ok, calculating absolute energy density is problematic in QFT. But, actually not this is what I want to calculate. I want to calculate the difference between the energy density of my pet higgs field and the vacuum state. Does it not make things easier?

Stupid question inc

user image

How was this explaination derived in first paragraph

why F is that way?

I know it's from the limit but doesn't seem obvious to me

I mean as the limit of distance goes to infinity the force becomes approximately same as the total mass of that bounded mass system

but how you derive this?

sorry I am in hurry cya

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