3:16 AM
@ACuriousMind there's lots of us in germany
probably unrelated

1 hour later…
4:39 AM
@RyanUnger I cycle past a business called Ungerer every day in Chester. I've often wondered if the two surnames stem from a common root.

3 hours later…
7:21 AM
Sonthe question now is
If the automorphism group contains a lie subgroup
Is there an associated principal bundle of that Lie group
As long as it's defined over the entire manifold anyway
Also is that only true for the internal part
Ie the group $\Lambda(p)$

2 hours later…
9:16 AM
Recent 'Solution of the Navier-Stokes equation' drama ("Unfortunately, the proof proposed by the author is incorrect. It is based on a Gronwall-like inequality...")
@Slereah it's just a coordinate transformation man

@bolbteppa That's a gauge transformation you swine

Kinda cool, that the interpretation that measurements splits into quantum realities, and then these realities themselves are entangled, thus only those that correlated to each other can merge again to form the correlated outcome

"The functional $J_{\gamma}[y] = \int_{x_0}^{x_1} F(x,y,y')dx, \ y = (y_1,...,y_n),$ where $\gamma$ is a curve described by $y = y(x)$ on $x_0 \leq x \leq x_1$, is said to be invariant under the transformation
$$x^* = \Phi(x,y_1,...,y_n,y_1',...,y_n') = \Phi(x,y,y'),$$
$$y_i^* = \Psi_i(x,y_1,...,y_n,y_1',...,y_n') = \Psi_i(x,y,y'),$$
carrying $y = y(x)$ on $x_0 \leq x \leq x_1$ into $y^* = y^*(x^*)$ on $x_0^* \leq x^* \leq x_1^*$, when $J_{\gamma^*}[y^*] = J_{\gamma}[y]$, i.e.
$$\int_{x_0^*}^{x_1^*} F(x^*,y^*,y'^*)dx^* = \int_{x_0}^{x_1} F(x,y,y')dx."$$

Problem is, said paper does not seemed to exist as the actual journal have no trace of the name of the two authors

What's wrong with this

10:02 AM
@bolbteppa not fancy enough
I mean, that should be about the same thing in the end, really
I'm not sure if I can generalize the thing to both fields and extended objects, though
Is there some generalization that includes both the space of bundle sections and the space of embeddings?
Something which can describe both $\Gamma(E)$ and $\text{Emb}(\Sigma, M)$

10:54 AM
A relatively old but interesting paper
NewScientist recently interviewed him on this
There may be possible super quantum mechanics because intermediate size entangled systems may happened to correlate with some similar system on the other side of the galaxy, resulting in outcomes that deviates from the Born Rule

11:28 AM
This suggestion, kinda reminds my discussion with semiclassical some time ago, on how the ontology of bohmian trajectories, may open up an interesting possibility to take advantage of quantum potentials already present in the environment that is located far away from the laboratory, to guide the experiment trajectories to their desired place and to map the environement's wavefunction
The way events fuse to give new events of higher diversity also reminds of the philosophy discussion I had in uni on the nature of creativity, which abstractly, can be said to be lots of pre potentialities intersect like lines in a vast space, and produce a potential new idea that can then be actualised, or a plane where there are many expanding white spheres, and whenever they intersect, a new sphere grew at the intersection, take traits of all those involved
It also reminds of that philosophy of time discussion in last week's newscientist event, and that this model may be compatible with that model of time where the flow of time is produced by how we arrange information in our brain in a sequence
It also reminds of causal dynamics triangulation and tensor networks in quantum gravity (and indeed, their model also have traits of those theories)
Finally, I wonder what will happen if we nuke postulate 3 and allow causality to flow backwards...
pinging @vzn because he love superquantum mechanics

hmmmmmmmmm
> # Yahoo bot is evil.
-- Stack Exchange
more to the point, it allows indexing of some transcripts but it bans trawling through the /users/ directory

11:48 AM
7

After reading and commenting on this question PHP Library for Keeping your site index by Google, Bing, etc, I was curious to look at StackOverFlow's sitemap. This returned a 404 error which I am guessing is just a protected page by determining if your are a Index Bot or simply doesnt exists. ...

@Secret that does look like a ten-year-old April Fools joke, though
=P

12:06 PM
0

I just read this argument in this paper (PDF). It suggests that, from variational principles, you can show that you can always lower the energy of a state by making the phase constant, thus resulting in a ground state that must have no phase change. I know this to be true for 1D systems (ground ...

@Qmechanic I swear there's a duplicate somewhere
either here or on MathOverflow
and I'm also vaguely confident that you answered said duplicate
or maybe not exact duplicates, given the precise details of what's being asked, but extremely close

12:56 PM
Hm

2 hours later…
2:34 PM
Have mercy nlab

If the order of field isn't defined then what do I take it to be
Like R is single tuple
$R^{2}$ is 2
What about $C$

what do you mean

3:08 PM
@Slereah what does Aut(Emb) mean

Basically I want the set of transformations on extended objects
So it is the set of automorphisms of embedding of one manifold in another

I don't know what that means

for instance let's say $\mathbb{R}$ to $\mathbb{R}^3$

can you just define Aut(Emb(M,N)) please

Hm
Tricky one because I'm not sure if there's any specific property it should preserve
I guess the group of maps between all such embeddings

3:15 PM

Alas
Tried looking up things on the topic but not quite sure what to google
Pretty sure that if anything it is just diffeomorphisms on both manifolds

@Slereah those would be the inner automorphisms I think
idk what the outer ones would be
but idk what Aut(Emb) even is so it's hard to help

Well as I said
I basically want to have all the possible transformations of a submanifold
So that it remains a submanifold
So that I can get all possible transformations on ie, point particles or strings
For instance for let's say R in R4, get all non-self intersecting curves out of it

@Secret hi whats new? a paper coauthored by smolin, legendary contrarian. have read some of his ideas, he has a new interview in quanta. cant yet feel close resonance with his research directions but think hes ahead of the pack in some slippery-to-pin-down ways. believe hes very close to discovering fluid paradigm under different terminology. leveraging google, here black box ML algorithm (philpapers) finds information flow in related papers to his. philpapers.org/rec/SMOTDO-2

3:34 PM
well, an ensemble of events recovered the quantum potential, which has a fluid like interpretation
it will be more interesting on how uncountably many far away but very similar events (and hence has to be in a superposition in some way according to his postulates) behave, because then we can truly get serious on a nonlocal causal fluid which spacetime then emerge from it
I wonder what properties will that kind of spacetime have, a spacetime made entirely of these superquantum units...

the ideas remind me of some of wheelers directions about information as a fundamental quantity and geometrodynamics, the influence is detectable. smolin also seems to have some affinity for bohmian mechanics. on other hand he seems to invent a lot of new concepts.

Typical of Smolin. He has a wealth of ideas from background independent physics to universe under Darwin evolution
I like when people invent new concepts. Getting stuck in the status quo can get stagnant
But one also need to be cautious, like those dark matter theorists have invented a zoo of particles, but they all basically are variants of the same thing
and none of them show up in the detectors so far (other than a sinusoidal modulation of unexplained nature)
Some recent trends are more encouraging, such as going beyond the axion and WIMP paradigm, and start thinking about larger scale effects

> Fundamentally there are amplitudes for causal processes in energetic causal sets, but no space-time. An embedding of the causal processes in an emergent space-time arises only at the semiclassical level. Hence, fundamentally there are no commutation relations, no uncertainty principle and, indeed, no ℏ.
> All that remains of quantum theory is the relationship between the absolute value squared of complex amplitudes and probabilities. Consequently, we find that neither locality, nor non locality, are primary concepts, only causality exists at the fundamental level.

I think its more important than ever to talk about the philosophy of physics. So many puzzling findings recently that defy comprehension, and philosophy may be the missing component
That's one reason I enjoy reading these background independent physics models. It free us from the constraint of spacetime to think of something more radical

3:56 PM
oh wow missed his recent book blurb. am sold, gotta buy this asap. borderline radical povs very similar to many espoused by me, great minds think alike, the naysayers/ skeptics are gonna freak/ flip out/ have seizure :) :P Einstein’s Unfinished Revolution—THE SEARCH FOR WHAT LIES BEYOND THE QUANTUM / By LEE SMOLIN penguinrandomhouse.com/books/316818/…
> In Einstein’s Unfinished Revolution, theoretical physicist Lee Smolin provocatively argues that the problems which have bedeviled quantum physics since its inception are unsolved and unsolvable, for the simple reason that the theory is incomplete. There is more to quantum physics, waiting to be discovered.
> Our task–if we are to have simple answers to our simple questions about the universe we live in–must be to go beyond quantum mechanics to a description of the world on an atomic scale that makes sense.

This one is not as radical, but it tries to derive a bell theorem for general probabilistic theories, including quantum mechanics
One of the most interesting philosophy of physics often came from the quantum mechanics of time and other complete overhaul of time models

Hi guys I just found this equality, do somebody know if this is true and how can I prove it?

4:37 PM
@Runlikehell this is an old and useful identity, which can be said in a few ways e.g. det(exp(A)) = exp(tr(A))
that last one is pretty intuitive I think. for a few different proof methods see this MSE question: math.stackexchange.com/questions/1487773/…

4:53 PM
This HNQ sorta makes me giggle: "Why don't they build airplanes from 3D printer plastic?" Last sentence of top answer: "So the brief answer is, they don't build airplanes from 3D printer plastic (or clay, or plaster, or thatch) because they want them to fly."

@Semiclassical Thank you

@Semiclassical that post's score is remarkable
+6 -3
I was expecting +36 -33

yeah, a lot more attention on the answer than the question

happily I can downvote on Aviation, courtesy of this ridiculous thread
(also from HNQ)
though I suspect this one also got selected by the Algorithm?

5:00 PM
I like how that answer amounts to: "because mercator projection (or whatever projection they're using) is worthless near the poles"

yeah
also "no, that's not the Atlantic, look again"

lol, that too
i mean, there is a reasonable question in there: what factors go into determining an airline's trajectory besides geodesic distance?
but the way it was posed was pretty silly
converting FlightAware data into Google Earth data is really neat tho

I wonder how our flat-earth user would have explained it.

FlightAware is clearly part of the conspiracy

> Although you specifically mention 3D printing with plastics, 3D printing with metals is a growing field. Some boutique automotive companies are using 3D-printed titanium engine parts, because they can print structures that aren't achievable with machining, to reduce weight. Although this field is still immature - AFAIK there are no aviation-certified metal printers yet - you'll be flying with metal, 3D-printed aircraft parts within the next decade.
I can do him one better

5:10 PM
neat
of course, there's a big difference between "some" and "all" of the parts being 3D-printed

I don't know whether metal 3D-printed flight-critical hardware is in use in aviation, but if nothing else the Electron rocket uses the Rutherford engine, which is mostly 3D printed. — E.P. 10 secs ago
screw cars
(at a minimum)

there you go

@Loong you should add it there as a comment
> AFAIK there are no aviation-certified metal printers yet
depends what you mean by aviation, it seems

So this is another question where, beneath the silly exterior, there is a good question underneath

5:19 PM
@Semiclassical eh
I'm unconvinced that the question below it (without such issues) wouldn't have provided an equally rich set of answers

There's good reasons why you wouldn't see 3D-printed plastics in aviation, but 3D-printing as a whole is relevant

5:54 PM
Hm
If I want my field theory v. embedding thing to give the same set of transformations for point particles
What should the subset of transformations be
I don't think that would work for every transformation

2 hours later…
7:29 PM
Are my calculations correct according to the true result?

1 hour later…
8:41 PM
a good first step would be to rotate that picture

9:20 PM
@Qmechanic I have seen also the book Goldstein
@Qmechanic And I think that $\epsilon$ is $-mc^2$.

9:43 PM

@Sebastiano what's the issue

@bolbteppa Hi, they are any images for my recent question. I can not put image into my question.

Basically the relativistic action is $S = - c \int ds$ where $ds = \sqrt{\dot{x}^2} d \tau$ and $c$ is some constant which we determine by going to the non-relativistic limit which should give us the non-relativistic action, this is explained in Landau vol. 2 ch. 2
Pretty sure that $\varepsilon \Psi$ should be $e \Psi$

@Sebastiano You have been told before (with reference to this post) that we much prefer typed text and formulae over screenshots. Posting the screenshots in chat where they are not even linked to the question for other users is even worse. Please do consider making the effort of actually typing out the material you want to quote if you want others to invest the effort of answering your question.

@ACuriousMind I have only put several images as citations into chat. At this moment I'm editing my answer with other references.

9:53 PM
To the relativistic action $S = - mc \int ds$ we add $- \frac{e}{c} \int A_{\mu} dx^{\mu} = - \frac{e}{c} \int (\phi,A_i) \cdot (c,c \mathbf{v}) d t$ which is your action with $\varepsilon = e$

@bolbteppa Can you put, an answer, please into my question? Thank you very much for your effort. I wanted an answer so I don't have to remember what you wrote in the chat room. Thank you very much.

@Sebastiano I would delete it, has nothing to do with the twin paradox for example, you should remember it and read the reference I gave :p

@bolbteppa You're authorized to change the title of my question. Approved your idea :-)

Read the reference then write it up yourself, good exercise

@bolbteppa ok thank you very very much.