@0celo7 : BECAUSE I DON'T KNOW

I guess it's possible???

D:

well who would know

Jesus

how are forces in GR defined, anyway

It's all that is left in the equation of motion after the geodesic part, I suppose

exactly

but how does one get it from a variational principle

I think it's still $\partial L / \partial \phi$

hmm

what is the action of a particle in GR

Point particle?

ya

$S = \int d\tau \ \frac{m}{2} g_{ab}(x) \dot x^a \dot x^b$

un-free particle

Well you can add a potential

$V(x)$ or whatever

Yes! What does it look like

$\int d\tau \ V(x)$ I suppose

Although

The kinetic part is already dependant on $x$

Which is the gravitational force, technically, I s'ppose

Hm

I don't think you can describe non-gravitational forces just by variation alone

nothing about this in MTW?

Hell if I know

@bolbteppa : Who told you Lagrangian mechanics involves a concept of energy via symmetries? Lagrange predates Noether, the Lagrangian is to do with energy difference as opposed to the energy conservation of Newtonian mechanics.

@Slereah we need to ask some questions on this

for science!

@bolbteppa : defining work in terms of forces and linking that to energy via the work-energy theorem won't help you to understand what energy is, or that its the fundamental thing from which matter is made. Why don't you ask a question about that?

@JohnDuffield I can prove it for you if you'd like, but here is a statement of it for example physics.stackexchange.com/a/3017/25851

Maybe instead you should ask the real questions!

Like what is the determinant in Pauli Fierz theory

@Danu Almost done with Kahneman! Great book!

Note he took care to point out "accurate definitions" i.e. was ready for obfuscation by people who want to obfuscate

> Centuries ago, before people appreciated the fundamental role of maths in physics, they believed e.g. that the heat - a form of energy - was a material called the phlogiston

@JohnDuffield you can read a bit more on this here motls.blogspot.ie/2010/08/…

Phlogiston?

@0celo7 oh you're quoting my links now despite our apparent agreement not to interact, next you'll ask me about Maupertuis...

That has to be the coolest word.

According to Feynman it is $\sqrt{-g} = \sqrt{-\eta} e^{\frac{1}{2}Tr(\ln(\delta^a_b + h^a_b))}$

@Slereah What is this Feynman paper

It is not

It's Feynman's lecture on gravitation

Although

@bolbteppa Nope, you'd likely use linear algebra that goes way beyond me.

@Slereah where?

It might also be in his paper on QG?

Last chapter

@0celo7 Meta-humor... good!

Also, I think traces should be typeset as $\operatorname{tr}(X)$

no capital letter

@Danu indeed

Over my dead body

@Danu Good?

I've succeeded if even comments at me end up working the opposite way

@JohnDuffield my point to you was to encourage you to read better books, I'm guessing you got that definition of energy from high school books

Hm

@0celo7 : here's your citation: Does the inertia of a body depend on its energy content?. Pay attention to this: "The kinetic energy of the body with respect to (ξ,η,ζ ) diminishes as a result of the emission of light, and the amount of diminution is independent of the properties of the body. Moreover, the difference K0 − K1, like the kinetic energy of the electron (§ 10), depends on the velocity."

That's one infinite sum for the determinant and one infinite sum for the inverse metric

Note the mention of body and electron on the same line.

Dang

@JohnDuffield Sigh, Einstein had no clue about the Higgs, so don't quote him in this context.

Is that a BSoD?

Lol

More importantly

Is that you in the reflection

@Slereah Yes

I know I need a hair cut

@JohnDuffield giving incorrect circular definitions of energy wont help you understand it, I just showed you how your definition was flawed in what I said, historically the concept came from force before electromagnetism was worked out, let alone quantum mechanics etc... Newton's law is a local form of the global Lagrangian/Hamiltonian mechanics, so any definition of energy from Newton's law is just starting from a certain place, you can glean some insight from it if you think about it...

@bolbteppa : Avoid debating with Duffield

It is not really going anywhere

Well I'm just trying to show him how his definition is a patently false strawman and to encourage him to read better books so he can formulate his arguments and thoughts more clearly

@0celo7 : the point to appreciate is that E=mc² is not wrong. And nor is the wave nature of matter. Ergo you should be able to work out from [the photon in the mirror-box that that photon momentum is a measure of resistance to change-in-motion for a wave propagating on an open path at c, whilst electron mass is a measure of resistance to change-in-motion for a wave propagating in a closed path. It's that simple. That's why the mass of a body is a measure of its energy-content.

See arxiv.org/abs/1508.06478

Maybe it wont go anywhere though :\

@JohnDuffield Is the Higgs a myth?

"since it definitely carries momentum and energy, it has non-zero inertial mass ... and so, light must be heavy"?

@bolbteppa : I kind of got it from the stress-energy-momentum tensor, which "describes the density and flux of energy and momentum in spacetime". Note the energy-pressure diagonal. It's like space is modelled as this gin-clear ghostly elastic, and you inject more of the same to create a surrounding pressure gradient. Only you added energy. So you at the fundamental level you have difficulty in distinguishing space and energy.

>gin-clear ghostly elastic

what

John is like a politician, same talking points over and over again.

@Slereah Why gin, I wonder. Why not water or vodka?

vodka means water

@JohnDuffield I don't know what that was responding to, but there is a stress-energy-momentum tensor when you analyze the motion of a particle moving in an electromagnetic field, there is a stress-energy-momentum tensor when you analyze how the geometry of space reacts to some matter and energy in that space, I think you are letting mathematical terminology get the better of you and running away with a hint of what it says, rather than carefully going through the details

H2O

vodka = H2O + Russian H2O

@bolbteppa : You fool

You are falling for the trap

haha

@0celo7 : it's not a myth per se, but there's a lot of myth surrounding it. The Higgs mechanism is said to be responsible for only 1% of the mass of matter. And it isn't responsible for the mass of what's described as the Higgs boson. The lifetime of which is so very short that it hasn't actually been observed. Instead its existence has been inferred from the decay products.

So a photon is a trivial knot?

11:40

Too bad my question got deleted

I still think it was good

@bolbteppa : light is heavy in that it has a non-zero inertial mass. Hence "radiation conveys inertia between the emitting and absorbing bodies".

>1905

@JohnDuffield The Higgs only accounts for 1% of the electron mass?

@JohnDuffield are you using $E = mc^2$ to justify that light has inertial mass?

@bolbteppa : no, a photon is a wave.

Again I don't know what that's responding to

But are you using $E = mc^2$?

@bolbteppa trivial knot

@bolbteppa : no. The photon energy is E=hf, inertial mass is a measure of energy rather than mass. The mass in E=mc² is rest mass, not inertial mass.

I thought we had an agreement...

Not when JD is around

I'm referring to Einstein. What's not to like?

Hm

Does $E=mc^2$ apply to photons?

How does the spin statistic theorem work when you have no Fock space

@Slereah huh?

Well there's no Fock space in an interacting theory

@0celo7 : no, E=mc² does not apply to photons. E=hf applies to photons.

Hence no notion of individual particles

@JohnDuffield well the problem with referring to Einstein is, where did $E = hf$ come from?

So you can't say that the hilbert spaces are symmetrized

or antisymmetrized

I mean in the end the spin statistics theorem just depends on the commutation relations I suppose

@JohnDuffield Ok, so $E=mc^2$ does not apply to photons. Then how does the electron, which you claim is a photon, have mass?

But I wonder if there's a theorem for the non free case

ask @ACuriousMind

@bolbteppa E=hf came from Planck. He's the guy who was the editor of Annalen der Physik.

@JohnDuffield and where did Planck come from? Are you aware he was assuming quantum field theory assumptions in his calculation?

> Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen

@ACuriousMind Are all German titles this long?

@JohnDuffield In other words, assumptions that cannot be justified except for using quantum field theory, otherwise it's witchcraft, I thought you were skeptical of unjustified assumptions, you seem to prefer authority to assumptions here

@0celo7 : because the mass of a body is a measure of its energy-content. The electron is like the photon going round and round in the box. Minus the box.

@JohnDuffield What's the equation for that?

@0celo7 : A lot of science titles are way too long

@Slereah what should the title of our GR book be

"on analytic and algebraic topology of locally Euclidean parameterization of infinitely differentiable Riemannian manifold'

@JohnDuffield section 1.1 of Schwartz 'Quantum Field Theory and the Standard Model' goes through this and explains where the qft assumptions lie if you are curious as to why you are assuming things you shouldn't assume

@0celo7 : It should have Geometrodynamics in the title

@bolbteppa : huh? Witchcraft? Resistance to change-in-motion along with pair production, the wave nature of matter, and annihilation isn't witchcraft.

@Slereah I can live with this

> Witchcraft

That's the best argument

Burn the witch!

@0celo7 : E=mc² isn't witchcraft either.

@JohnDuffield please answer my question

@0celo7 : go look it up. When you understand the mass of a body is a measure of its energy-content and take note of electron and body on the same line, you'll be able to work it out. Electron-positron annihilation is like opening one box with the other, whereupon each is a radiating body that loses mass. All of it. And then it isn't there any more.

@JohnDuffield okay so you're saying the only equation that describes light is $E = hf$, which does not include a mass term, but an equation like $E = mc^2$, which does include mass, does not apply to light, however 'resistance to change in motion' means it has mass?

@bolbteppa : mass is ambiguous. There's rest mass, inertial mass, active gravitational mass, passive gravitational mass, relativistic mass, and so on. When we use the word mass without qualification we mean rest mass. The photon doesn't exhibit any rest mass because it isn't at rest. Unless its going round and round in the mirror-box, when it's effectively at rest. Then it genuinely increases the mass of the system. The box is harder to move when the photon is in it.

wait wait are electrons little mirror boxes?

Is it because of the article you've linked to?

@0celo7 : kind of. You make an electron (and a positron) in pair production. In atomic orbitals electrons "exist as standing waves" . That wave isn't propagating linearly at c, now is it? Instead we talk of spinors. Think of it as a 511keV photon trapped "in a box of its own making".

> Think of it as a 511keV photon trapped "in a box of its own making".

Please describe that mathematically

Just do that one thing for me

That's all I want for Christmas

Sorry @0celo7

Duffield cannot write any math more complicated than a division

what if it's linear algebra

then I wouldn't even understand it :o