Li likes to talk about himself in the third person

but there exist definite values that had definite values before the measurement, they just changed during the measurement. A point of the Coleman lecture is that it's "nonlocal realism" or "local QM", period.

@ViEsr

@0celo7 I'm not gonna argue with you that I was going to flag you for the blatant insults you wisely deleted.

@NeuroFuzzy Yes, but a wave function too doesn't exist then I guess

It is just a tool

?

Man

Trying to find a chinese paper isn't easy

The authors are Li, Xu and Liu

None of which are unique names at all

Trying to translate "Associated to a divisor is a holomorphic line bundle, to a meromorphic function a line bundle together with a holomorphic section, and to a line bundle its Chern class", I hopefully see that a meromorphic function has a line bundle of derivatives to it, and that the collection of derivatives has a Chern class which is just some way of determining twitstedess as in Mobius V Cylinder.

But coming from the other angle, some notion of polygons is associated to a collection of derivatives somehow. Weird...

@ViEsr I agree and disagree... the angles/positions of a rigid body in classical mechanics also don't exist, and are just mathematical tools.

Yes, but somethings exist

Like say momentum

We believe a particle is actually carrying it

or a field

which itself is present

"Since a compact complex manifold admits no global holomorphic functions, we might rather expect its structure to be reflected in the global meromorphic functions and related linear systems of divisors on the manifold"

@bolbteppa I'm going to maintain that this seems weird because it has nothing to do with derivatives at all ;) The correspondence divisor <-> line bundle, section of line bundle <-> function with poles and line bundle <-> Homology class is completely general.

@ViEsr Well, if you know anything less than the wavefunction you can't totally predict its state in the future. And if you toss out local realism as suggested then there is nothing more you can know than the wavefunction

Maybe I'm not giving what you say enough credit, though.

But if you are analyzing $y = f(x)$ it's line bundle is the collection of derivatives along the curve, why does that dissappear for complex functions?

"A space with a complex metric permitted by quantum cosmology is given; two regions, one containing no closed causal curve and one containing closed timelike curves, are separated by a complex region. Through quantum tunneling one can travel from one region to the other. The vacuum polarization stress-energy tensor converges everywhere so the space is stable. This challenges Hawking's chronology protection conjecture and highlights on building a time machine."

If you have to put in a complex metric, maybe it is not that challenged

"Through a quantum process, a complex geometry might be created *from a Lorentzian geometry."

A tad hopeful

@bolbteppa Well, it doesn't disappear. You can probably still construct the thing explicitly with Dolbeault differentials or something. It's just that the phenomenon is far more general. But I've got a feeling that you are trying to do something completely different from what I'd do here, so I'll shut up about it now

"I construct a spacetime with closed timelike curves and without closed causal geodesics."

Heyyy

That's the answer to my SE question, maybe!

"the renormalized stress-energy tensor of vacuum fluctuations should not diverge because there does not exist a closed null geodesic which is the origin of the divergence"

Seems to be it, yes

He cheats a bit by making it a spacetime with boundaries, though

Hm wonder if there's a theorem specifying that the Cauchy horizon of a non-chronological spacetime always has closed null curves

(that are geodesics)

Guys, is there really a particular paper layout for crazy people

Or is my heart just cold and filled with hate

I don't know why but it seems most crazy people fear using LaTeX

That is completely and definitely true.

(based on anecdotal evidence)

It's kind of "I want to imitate real science paper but I only know how to use Words"

Just remember the evidence of Einstein is not anecdotal :P

This fellow thinks string theory and supersymmetry are elements of fringe science.

I chewed him out for that.

naught but woo

@HDE226868 Uh, I'm not even sure it is supersymmetry and string theory he called fringe science in there, but that answer is just gibberish.

> I figured I might go outside of the box (fringe science?!). I think the theory is called supersymmetry which I guess could turn what we know upside down?

Well, the "?!" might indicate hyperbola/tongue-in-cheek phrasing :P

It's completely unclear what supersymmetry has to do with anything there, though

I think he just wanted to impress with his science mastery

You know

I'm not quite sure those papers on string theory in a CTC background are quantum things

I wonder if it's classical NG action

My Physics book I'm reading right now is saying that because the field of a bar magnet is not uniform, the magnetic dipole in an an unmagnetized iron nail is attracted to it, but wouldn't it also be attracted to the magnet if it were uniform as well?

Hm

More shameless advertising for collaboratively solving all the problems in Van Kampen's stochastic processes book.

Apparently replacing CTCs with their covering space, when possible, leads to singularities

Already got one other collaborator. Making fast progress, i.e. a few problems per night.

Join in the fun!

Although apparently that's only for contractible CTCs

I guess that it's pretty easy to unwrap the torus spacetime

Seriously, I will even fund a copy of the book for anyone interested!

I don't know stochastic stuff man

I don't want to, that might increase the GDP

@DanielSank Uh, can you wait a few years?

I probably need to know measure theory, Calc variations, PDEs, etc.

Oh wait

I guess contractible vs. non-contractible is a better classification of CTCs than "topologically trivial"

Basically the same

except more accurate

@Slereah What other notion of "topologically trivial" were you considering?

Well I wanted a nice term to say "This CTC does not stem from a topology trick"

But even in a non-trivial manifold that could still happen

So contractible is a much better notion

What is a topologically trivial in this case

Well the manifold

aka $\mathbb{R}^n$

but it was not exactly the notion I wanted

Oh it's globally homeo to Rn

It's just the boring manifold

Hey, topology question

Is a manifold that can have one coordinate chart always $\mathbb{R}^n$ with holes in

Come again?

Is there any topology that you can get other than $\mathbb{R}^n$ with a countable number of points removed if you have only one coordinate chart

@Slereah No, by definition of a chart, existence of a global chart means that the entire thing is homeomorphic to $\mathbb{R}^n$.

I don't even see why you think you can remove points

Well because the chart is only to open sets of $R^n$, no?

Not necessarily the entire manifold

Hm, well, depends how you define "global chart" or "chart" in the first place.

A diffeomorphism between the manifold and an open set of $R^n$?

Because pointwise, the definition "there is a neighbourhood homeomorphic to an open subset of $\mathbb{R}^n$" is equivalent to "there is a nhbd homeomorphic to a connected open subset of $\mathbb{R}^n$ is equivalent to "there is a nhbd homeomorphic to the open unit ball in $\mathbb{R}^n$".

Can we replace the shorthand for neighbourhood by "neigh."

That way it sounds like we are horses

For a "global chart", the answer to your question depends on which of these you want to make global.

Just call it hood