The h Bar

10:04 PM

“You can not touch an idealization.”

@ACuriousMind Ok, no gravity. But then I still want diffeomorphism invariance of my tensor fields. While calculating their induced action on those fields, I'll notice the appearance of this GL(n) action on the tangent space. If the manifold is curved, the covariant derivative will bring in the connection. Now you could argue that, nope the manifold is just curved, no gravity. I would answer that this curvature IS gravity, for which you are neglecting the backreaction to the fields.

Slereah

Flat manifolds can be diffeomorphism invariant

Minkowski space is still diffeomorphism invariant

G. Bergeron

@Slereah Yes, and that means neglecting gravity

ACuriousMind

@G.Bergeron Where does the connection come from?

G. Bergeron

@ACuriousMind The covariant derivative on a curved manifold

ACuriousMind

10:09 PM

@G.Bergeron What would I need it for if I'm doing, say, Yang-Mills?

G. Bergeron

@ACuriousMind Well then spacetime is flat and hence there is no gravity

ACuriousMind

Why would spacetime be flat?

I can put a Yang-Mills theory on some arbitrary curved Riemannian or Lorentzian 4-fold

The action still works, you don't need to modify it

Slereah

@G.Bergeron Remember that the curvature and the connection are two different things!

G. Bergeron

@ACuriousMind How will you define $\partial_\mu$ from the Yang-Mills action, then?

@Slereah I know, but you get one from the other

If you use the metric connection

And if not too actually

ACuriousMind

@G.Bergeron The Yang Mills Lagrangian is $\mathrm{Tr}(\mathrm{d}A \wedge {\star}\mathrm{d}A)$. This is fully diffeomorphism invariant and only needs the metric for the Hodge star, but neither curvature nor Christoffels

That is, the exterior derivative is a perfectly fine operator regardless of curved space because the terms that spoil the proper transformation as a tensor for the ordinary derivative are canceled by the anti-symmetrization

G. Bergeron

10:14 PM

@ACuriousMind Ah that might be it

@ACuriousMind When written of the exterior derivative, it seems legit :p

@ACuriousMind But what about your other fields? I mean like the one that carried that global gauge group action in the first place?

Those were the ones I had in mind

ACuriousMind

@G.Bergeron Pure Yang-Mills has no other fields, just like electromagnetism in a vacuum

But you can add other fields, this isn't anything special - you don't need the covariant derivative to build actions that work for curved manifolds, any $\phi^n$ theory also works

G. Bergeron

@ACuriousMind Fair enough, I don't think we disagree on that case.

ACuriousMind

For instance, the free scalar field is also just $\mathrm{d}\phi \wedge {\star}\mathrm{d}\phi + m^2 \phi \wedge {\star}\phi$ in its Lagrangian.

G. Bergeron

@ACuriousMind I think I might need to explore FTs in a coordinate free setting now. I know the math well and I know FTs from the usual treatment.

ACuriousMind

Or couple the YM theory to a current - the term is just $A_\mu J^\mu$, or $A\wedge {\star} J$.

No sign of any connection or curvature there

G. Bergeron

10:22 PM

@ACuriousMind Of course

@ACuriousMind How would you reconnect this observation with the appearance of a covariant derivative when writing everything in a coordinate system. Problematic terms always cancel like above?

Also: WHY do they not teach QFT in a fully coordinate-free and geometrical setting at the outset!!!

ACuriousMind

@G.Bergeron Yes, since there is a coordinate-free way to write everything without a spacetime covariant derivative, it is guaranteed none will appear in any explicit coordinate expression. You need to be careful not to try and take summands in the coordinate expressions as meaningful objects (like $(\mathrm{d}A)_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$ is a proper tensor, but $\partial_\mu A_\nu$ is just a coordinate-dependent expression without coordinate-free meaning)

G. Bergeron

After learning proper diff geom, I just see so many cases of huge technical computations in QFT reduced to simple and direct ones in the coordinate-free formalism...

ACuriousMind

I'm with you there :)

vzn

← thinks there is something off about idea of "meaninglessness" of certain coordinate systems in/ wrt GR curvature etc, maybe overturning this concept-bordering- on-bias key to new theory

G. Bergeron

@ACuriousMind So then you'd say gravity enters the picture only when you ''gauge the connection and add the proper terms to the action''?

@ACuriousMind I would have seen the cases you where describing as basically including gravity, but while entirely neglecting the reaction of the metric to the presence of the matter/yang-mills fields.

@vzn Coordinate-free differential geometry is really REALLY nice! You directly grasp the ''meaninglessness'' of the coordinates choice.

vzn

10:35 PM

@G.Bergeron not an expert on GR and not following your conversation in detail, it reminds me of a line from this recent JR answer which sounds "questionable bordering on suspicious" to me physics.stackexchange.com/questions/399738/…

> The point is that the coordinate speed of light depends on the observer and has no absolute meaning.

ACuriousMind

@G.Bergeron Well, gravity enters when you promote the metric to a dynamical field and add the E-H term to the action. The connection enters by observing that you can - by exact analogy with minimal coupling in other gauge theories - write the equations of motion in curved space (no matter whether you added the E-H term or not) as those in flat space with the ordinary derivatives replaced by spacetime covariant derivatives.

bolbteppa

I think even electromagnetism in a coordinate-free fashion is terrible tbh, but there are some advanced things which seem to become simpler, e.g. KK stuff

G. Bergeron

@bolbteppa If the goal is to apply it to build, say, an antenna, then yes, but if the goal is to understand the structure of EM, than I strongly disagree!

ACuriousMind

Note that these are two different things: One might introduce the spacetime covariant derivative without promoting the metric to a dynamical field. You might call this "ignoring the backreaction" of the fields on the metric.

G. Bergeron

@ACuriousMind Well yes, anyway writing everything in a coordinate-full fashion will force one to introduce the connection. I guess that was my initial point. I did not realize this connection will entirely cancel out of the actual action you end up writing (which is kind of obvious after the fact...) TIL!

ACuriousMind

10:43 PM

@G.Bergeron Yeah, that's a neat summary

G. Bergeron

@vzn Absolute means universal to all observers...

0celo7

What is going on

G. Bergeron

@vzn coordinate speed is not a 4-vector hence its contraction does not mean anything.

@0celo7 Life, I guess

Also, my asynchronous exchange with ACM is kinda wrapped-up

vzn

@G.Bergeron struggling to put this into words, but saying "coordinate speed of light has no absolute meaning" does not seem to be the same as "meaningless because there is no coordinate system universal to all observers"... there does seem to be a way to establish a "universal" coordinate system that is not meaningless. its maybe just not preferred or unique...

G. Bergeron

@vzn The central point is that if I can change the value of a presumably physical quantities by just changing the way I index events with coordinates, than it ought to not only describe the physics but also my specific choice of coordinates.

vzn

10:55 PM

@G.Bergeron am not contradicting GR as established but feel Tenev + Horstemeyer system is in fact a meaningful universal coordinate system for GR.

ACuriousMind

Well, I feel I'm 3 meters tall. Does that mean I'm 3 meters tall?

bolbteppa

My guess is you're saying that GR trying to frame things independently of coordinate systems, basically the whole point of GR, en.wikipedia.org/wiki/General_covariance , is "bias", and overturning it, i.e. demolishing GR, is key to a new theory, which is to completely misunderstand GR

G. Bergeron

@vzn Suppose you actually build a shared ''universal'' coordinate system. Then yeah, anyone might agree on the value of physical quantities wrt those coordinates, fine. But should that specific value have any meaning knowing that this value depends crucially on an arbitrary convention we set up?

vzn

ACM/ BT my ref to Tenev-Horstemeyer will make zero )( sense if you never actually read it...

@G.Bergeron a universal coordinate system can be an arbitrary convention among different "observers". its not a contradiction. T-H establish such a system.

bolbteppa

@vzn have you ever tried to go through these for fun theoreticalminimum.com/courses

All he really expects is a vague memory if the jist of calculus and not even really

vzn

10:59 PM

@bolbteppa if you ignore my refs, will feel free to ignore yours also. ps have susskinds QM book sitting on my pile.

G. Bergeron

@ACuriousMind @bolbteppa This Tenev-Hortemeyer paper is about a mathematical analogy between GR and continuum mechanics that seems to work out, but where establishing the equivalance principle is next to impossible as the matter cannot move in spacetime in this model (to be fair, the authors did hand-wave towards the quantumy wavelike nature of matter... eeek!)

bolbteppa

@vzn I didn't ignore your ref, I literally found the first equation in your paper in an elasticity book and the assumptions going into deriving it

G. Bergeron

@vzn Ok that call about the book is a non-argument, please.

vzn

@G.Bergeron it is not trying to be a TOE. the point is, it sets up a universal coordinate system for GR.

G. Bergeron

@vzn Which is not the problem per se, the problem is interpreting that universal coordinate system as being, well, physically fundamental.

bolbteppa

11:01 PM

arxiv.org/abs/1603.07655

vzn

@G.Bergeron they do not interpret it as "physically fundamental" except to call it the spacetime fabric or whatever... but actually maybe that is the point: they regard it as physically fundamental! (in some sense...)

G. Bergeron

@vzn Their paper is good and all as its primary goal is to setup this mathematical analogy in order to enable better computational methods.

@vzn And my point is that you can't see this as fundamental as it directly fail to illustrate the equivalence principle

vzn

@G.Bergeron think its obviously more than a (mere) mathematical analogy and that they say so in various places...

G. Bergeron

End of abstract: ''By introducing a mechanical analogy of General Relativity, we enable the application of Solid Mechanics tools to address problems in Cosmology. ''

vzn

@G.Bergeron it does not violate the equivalence principle. why would you think that is the case?

bolbteppa

11:05 PM

I don't know elasticity, but it definitely seems to me like equation 1.1 of your Tenev paper, the last link I gave, came from using Free Energy to link stress and strain in getting Hooke's law, and you simply need quantum statistical mechanics to justify free energy, so applying that to general relativity, as least to me, is really questionable without tons of caveats

G. Bergeron

@vzn Look, they might say this, although I don't remember it, but if they do, then they're just wrong. As for such a claim to be made, they have to treat the movement of matter!

vzn

@bolbteppa ofc its really questionable on conventional grounds. its nearly radical. but you cant disprove (any of) it.

G. Bergeron

@vzn No, they leave it ''as an exercise to the reader''

bolbteppa

ahaha

It makes no sense

What is free energy, if you don't know what quantum mechanics is

vzn

@bolbteppa you seem to be missing the fundamental, striking similarity, even near )( total alignment, with 1century old ideas of the ether.

G. Bergeron

11:07 PM

@bolbteppa I don't think this causes fundamental problem in the end as the physics of the fabric does not have to be relativistic to reproduce relativity.

@vzn Ether was ditched essentially BECAUSE of the equivalence principle.

vzn

@G.Bergeron the ether was ditched for multiple (valid! at the time!) reasons, the equivalence principle being a key one, michelson morley, etc. but dont throw the baby out with the bathwater™...

G. Bergeron

@vzn remember the equivalence principle equates gravitational mass with inertial mass. In order for that too make sense, there has to be the possibility of movement of matter for inertia to make sense.

vzn

@G.Bergeron do concede they handwave on what matter is doing in/ wrt their spacetime fabric, but myself dont see it as a unfixable difficulty/ inevitable contradiction. (have already sketched out/ outlined how it could work.)

bolbteppa

Equation 1.1 of your paper relies on thermodynamics for it's justification, without this thermodynamics justification you are basically using magic as your starting point, taking this as your general relativity starting point, or to say anything fundamental, makes no logical sense, on conventional grounds of making sense, yes it's really questionable based on this at least

G. Bergeron

@vzn Not inevitable contradiction, just a task of (apparently unfathomable for you) extreme difficulty to make it work

vzn

11:13 PM

@bolbteppa ok. highly questionable is not the same as wrong eh?

bolbteppa

I would say wrong, but I don't know elasticity well enough to be certain, but I would be shocked if it wasn't wrong

vzn

@G.Bergeron if it really is (all?) crap, think it should be easy to break it so to speak, to point to the fatal flaw that causes it all to crumble to dust/ nothingness.

bolbteppa

It seems like they are examining interesting analogies in the paper, not claiming what you are claiming the paper means

vzn

@bolbteppa see something (much) more than what theyve outlined, but aligned with it. have seen it for a very long time... see how it fits with other emerging theories etc, currently scattered around

G. Bergeron

@vzn Which it would if they give a description of matter movement

bolbteppa

11:15 PM

It vaguely makes sense you'd find some continuum mechanics behavior in spacetime when treated as a continuum

Emilio Pisanty

@vzn is the symbol combination )( intended to communicate something? If so, it's failing rather badly at that job.

vzn

@G.Bergeron ok. speaking of questionable, (as BT keeps insisting, his least deprecatory comments so far...) try asking yourself another question. how would matter behave that would make what theyve outlined so far work? have already mentioned some ideas on that...

bolbteppa

My guess is, by envisioning spacetime as a continuum, they (or you) are hoping to derive GR from continuum mechanics thinking alone, and the hope is some random continuum mechanics equation secretly encodes Einstein's Field Equations, but why is spacetime a continuum, why is spacetime even curved, how do you get from special relativity to this new thing without already setting up the seeds for GR

vzn

@bolbteppa turning that around (again), aka "trying to figure out what is tail vs dog", if you really think about it, the spacetime fabric concept they have outlined has all the seeds of GR. no offense, but you seem to be lost in all the castles of math/ concepts sometimes.

G. Bergeron

@vzn It would first need to be able to move in a rigid medium while inducing a modification of the density and elastic modulus of the same nature as how gravity is explained. But then this modification of the density/modulus has to be related to a variation of the fundamental forces (other than gravity) and for that to happen you need to put all of interactions (and hence all of physics) in the dynamic of that world-fabric

vzn

11:23 PM

@G.Bergeron now you are starting to get a glimmer of it. matter moves through the spacetime fabric not as a separate entity. its a density shift inside the spacetime fabric (apparently) with no ("measurable") "ether wind"/ doppler-type effects. there are major theories of matter that already work this way...

G. Bergeron

@bolbteppa Well continuum mechanics kind of does encode Einstein's equations, just not with the same interpretation and (this my point) without the possibility of such an interpretation.

s. patroller

::senses blackhole-of-productivity forming::

bolbteppa

The only way I know how to go from flat inertial Minkowski spacetime to GR is by examining non-inertial reference frames and basing everything on analogies to non-inertial reference frames, using behavior at infinity to distinguish, but you immediately get GR from this, so my sense is any continuum mechanics thinking is at best superfluous, but there is a bigger problem in that anything in continuum mechanics beyond basic definitions of 'stress/strain' relies on thermodynamics, which is quantum

G. Bergeron

@bolbteppa I agree about the superfluous-ness, but then I think one could potentially take continuum mechanics to be first principle (its still coherent). However, merging SR in that picture is where everything starts to crumble

bolbteppa

@vzn this is why those castles of math concepts are so important, if you are not careful you will immediately conflate thermodynamics (quantum mechanics) and general relativity blithely and 'put the cart before the horse', in your phraseology haha

vzn

11:27 PM

@bolbteppa they are probably not talking about "minkowski spacetime". honestly have to go look that up myself to figure out what it means... part of coming up with new theory is trying to discard "red herring memes"...

@bolbteppa there is a new study of quantum thermodynamics emerging, did you notice? am not aware of a deep connection between stress/ strain and thermodynamics, will have to take your word for it and look into it deeper. but again think there is a key concept of frictionlessness going on aka non newtonian fluid...

bolbteppa

Hooke's law

Hooke's law is a principle of physics that states that the force (F) needed to extend or compress a spring by some distance X scales linearly with respect to that distance. That is: F = kX, where k is a constant factor characteristic of the spring: its stiffness, and X is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ut tensio, sic vis ("as the extension, so the force" or "the extension is proportional to the...

vzn

lol yes they mentioned hookes law in my undergrad physics class and we had a laboratory experiment on it, can find wikipedia entries :P

G. Bergeron

@vzn Honestly suppose you try to make something entirely isomorphic to what know as of yet, you now face the challenge of having to build everything in one go (and that includes all the standard model forces) just so special relativity can be defined and be made to make sense. Now suppose you succeed, (not sure how that could even be done without bringing in QM already), then after all this work you wouldn't have brought yourself any closer to a theory of quantum gravity.

vzn

@G.Bergeron "honestly" you said you were interested in Big Questions™ like GR + QM. are you serious or not? did you think it would be easy? do you have a better idea? :P

G. Bergeron

@bolbteppa As the difficulties in doing so would not have been addressed at all but probably made even worse, and that is assuming you do not encounter problem already at the previous step as you try to bring in fundamental interactions in the spacetime fabric dynamic without bringing in QM.

vzn

11:35 PM

@bolbteppa dont forget springs have different amounts of friction and hookes law deals with an ideal spring that is not matched by real ones! due to dissipative forces... (the thermodynamics youre referring to?)

G. Bergeron

@vzn Yes, I am. And to do so, I consider my options. This one is not a nice one (it breaks any kind of nice constraints from symmetries) nor a promising one (the problem only seem to get worse) and if even possible will turn out to be of extreme complexity.

@s.patroller It formed ages ago... -_-

vzn

@G.Bergeron the path forward is not clear/ obvious to anyone but you can have more than 1 iron in the fire eh?

bolbteppa

What is friction, friction is a lie

vzn

@bolbteppa the new castles will be built out of the stones of the prior ones... (there will be both some dismantling + reuse...)

G. Bergeron

@vzn Following your analogy, it's more like humanity is massively dumping swords and battlecruisers and atomic bomb in the fire and at an industrial scale and you just came up with a kitchen wooden spoon...

bolbteppa

11:38 PM

I think you just went looking for things to support your conclusion, and you picked something which is too questionable, the fact you picked something like this with all these flaws should shock you into realizing things are a lot more complicated, and those towers of math are a guide to stop one making mistakes, not "bias" preventing us from seeing

vzn

@G.Bergeron physicists got a bit lost and wandered in the woods (still now!) when they abandoned classical mechanics and then told themselves it all made perfect sense... they did throw out baby(s) with the bathwater... einstein warned em but they didnt listen, thought/ said/ insisted he was crazy o_O

bolbteppa

I remember what it was like to try and understand advanced physics without any math, that was so scary and uncertain the math was the easy way out, it is for you too, will save a lot of pain tbh

G. Bergeron

@vzn And do note that I am NOT discouraging you to follow that path if you believes it leads somewhere, but the only thing I see on that path is a huge thorny mess that leads to a bottomless pit.

vzn

@G.Bergeron lol dont worry (many) others will help esp after certain milestones are reached. :) but yeah do wonder if it will show up in my lifetime at this rate o_O :(

bolbteppa

@vzn I am discouraging you from this path, I sincerely recommend you study these subjects properly

I really advise you to try those Susskind videos as a first step

vzn

11:42 PM

@bolbteppa lol Here There Be Dragons™

G. Bergeron

@vzn You realize you come to a board full of physicists (me included) to tell us we're all lost in the woods and we don't know what we're doing. It certainly is A possibility. Another one is that you underevaluate the difficulty of the problem / do not understand properly the constraints we have to work with.

Semiclassical

mèdeis ageômetrètos eisitô mou tèn stegèn

4

vzn

@G.Bergeron lol

bolbteppa

The Laplace-Runge-Lenz vector, and where it comes from, is very interesting for example

vzn

← beginners mind™ o_O :P

@G.Bergeron you guys are defn great fun to talk to even if you have no clue lol :P

bolbteppa

11:46 PM

I think you think we aren't capable of this kind of magical anti-establishment thinking, everybody is, this is the easy way out

vzn

@bolbteppa you guys are the establishment lol

G. Bergeron

@vzn Well, now you're being condescending, I'll go back to work on my debased and clueless physics.

bolbteppa

Feynman started accusing Einstein and Bohr and all them of being anti-establishment and saying that they had to defend the establishment, the establishment won btw

haha

vzn

@bolbteppa ?!? have no idea what youre talking about. feynman didnt seem to talk a lot about QM history or pay a lot of attn to its founders. he has a semifamous quote that he "didnt think there was a problem" etc

bolbteppa

The real problem is when these anti-establishment guys learn all the math and physics perfectly before trying to tear down the establishment, those guys are the real establishment breakers, the ones who don't learn it are great fun

vzn

11:50 PM

@G.Bergeron lol its only condescending if you have low self esteem :P

bolbteppa

Nope, Feynman very directly accused the older generation of being anti-establishment, and that the younger generation was far more conservative than them

vzn

@bolbteppa there were multiple "establishments" that were overturned. it gets difficult to keep track sometimes. the new establishment replaces the old one. whats that joke about young liberals and old conservatives?

bolbteppa

"In sharp contrast to the revolutionary attitudes of the older generation (people like Dirac, Bohr, and Heisenberg), the outlook of Schwinger, Feynman, Tomonaga, and Dyson was essentially conservative and pragmatic."

vzn

> If You Are Not a Liberal at 25, You Have No Heart. If You Are Not a Conservative at 35 You Have No Brain quoteinvestigator.com/2014/02/24/heart-head

bolbteppa

Tell that to the nobel prize winners

vzn

11:57 PM

lol 't hooft is 1 of my favorites, and he seems not unlike einstein in his establishment community credibility now... btw he might agree with some of these supposed "antiestablishment" ideas, along the lines of some of his research o_O :(

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