New math proves that a special kind of space-time is unstable | Hacker News Reader

New math proves that a special kind of space-time is unstable

quantamagazine.org

130 pointsfurcyd40 comments

Here is what I believe is the most relevant paper by Moschidis: https://arxiv.org/abs/1812.04268

I find it mildly amusing that this work is being done by mathematicians rather than theoretical physicists.

> I find it mildly amusing that this work is being done by mathematicians rather than theoretical physicists.

How so? This is very common. Math and theoretical physics are heavily interdisciplinary, and arguably the distinction between mathematicians and theoretical physicists is not as stark as most people would seem to think. At the highest caliber, the difference between a mathematician who works on physics and a theoretical physicist who works on math is a paper difference.

I don't think theoretical physicists would find these findings to be that interesting. There are a lot of mathematical results that can be somehow applied to physics, but very rarely something interesting comes out of it from physicists perspective. Obviously when it happens, then it can lead to a breakthrough as it happened when Einstein figured out how Riemmann geometry can be applied to GR.

The author himself is kind of uncertain if there are any real consequences comming out of his math:

>>The instability of AdS space-time has major implications for how we understand our own universe. First, since AdS space-time is unstable, it’s “something you will not see in nature,” Moschidis said.<<

>>But “even though AdS is not real,” he said, “it can still lead us to the discovery and study of real phenomena.” <<

I am not sure how our understanding of time-space can be increased by a theory that just does not describe reality.

Maybe the math is somehow useful? Maybe this might explain what happened after Big Bang (maybe instabilities were more common then)? Maybe this is the path to unify QM and GR (in the article it is mentioned that, but with some usual addition of not yet observed additional dimension that can explain everything - the feature of many "string" theories", that didn't give us much.

Theoretical physics has always studied theories that don't describe reality. It deepens our understanding of the theories that do describe reality. Eg., if you change one axiom of a reality-describing-theory and certain naturally occurring phenomena disappears, then you can say that that axioms causes that that phenomena to occur.

Also, this is not my field, but thousands of physics papers have been written on the AdS geometry (particularly the AdS-CFT duality). This line of thinking has brought a lot of clarity to string theory and to black hole physics.

It's definitely not the case that AdS being non-physical stops it from being useful in physics. ADS-CFT plays a big role in physics research today. I'm hoping that seeing how it breaks down will lead to clues about exactly where it diverges from the real world.

There's a long history of mathematicians working on general relativity; in fact, for decades general relativity was mostly the purview of mathematics, not physics, due to (1) the difficulty in finding exact solutions to the Einstein field equations and (2) their lack of physical meaning (eg, the Taub-NUT solution: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/196600...).

Didn't Einstien use Minkowski's geometry for his key theories? Seems like it's helpful to have a few mathematicians involved in the project.

Not really my field, but I think Riemann had more of an impact on Einstein in that he was looking for a mathematical structure that fit his intuition about spacetime, and he dug up a 50-year old theory and applied it to GR. My understanding is that Einstein was searching for a long time for the right tool, and went down a lot of dead-end paths, before he discovered Riemann geometry.

As I recall my history, it was actually believed that Einstein's first wife, Mileva Marić Einstein, who provided at least some of the mathematical muscle needed for GR [0].

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[0]: https://blogs.scientificamerican.com/guest-blog/the-forgotte...

I definitely agree he had a mathematician working with him to help, but am not sure it was his wife. I think that there's varying interpretations of her contributions to A. Einstein's work. If I'm remembering correctly, Walter Isaacson's Einstein biography tended towards says that she didn't truly contribute much to any of the work he did around that time, but that he did have a colleague or two formally trained in non-Euclidean geometries that he spent a lot of time working on GR with.

It was Marcel Grossman who introduced him to Riemman's work: https://en.wikipedia.org/wiki/Marcel_Grossmann

There is no evidence that his wife provided any of the "mathematical muscle needed for GR", nor is there reason to suspect that she would have been in a position to do so, since she was not a mathematician and had failed the undergraduate physics degree at the institute where she met Einstein (Einstein himself barely passed though).

[0] https://www.springer.com/gp/book/9781402039997

> If I'm remembering correctly, Walter Isaacson's Einstein biography tended towards says that she didn't truly contribute much to any of the work he did around that time....

I'm not sure how much credence I'd put in such an assertion given that Einstein himself wrote in a letter to Mileva:

> “When I read Helmholtz for the first time, it seemed so odd that you were not at my side and today, this is not getting better. I find the work we do together very good, healing and also easier.”

Emphasis added by me.

Having not read the book, Isaacson might have some additional evidence and insights I'm not aware of, but who knows?

> “When I read Helmholtz for the first time, it seemed so odd that you were not at my side and today, this is not getting better. I find the work we do together very good, healing and also easier.”

Note that this was written when they were both undergraduate students and would study together.

There are other examples in the SA article I posted, including a letter from 1905 where Einstein talks about their "work on relative motion."

Inspiring persistence.

I don't find this surprising at all. Theoretical physicists are really just applied mathematicians. I don't know a physicist that would disagree with this. In fact, many said Einstein was more a mathematician than a physicist.

Sort of. As a physicist I'd also say we have different sets of intuition, different willingnesses to play fast and loose or to make heuristic arguments (for a good example, consider the history of the Dirac delta function). Certainly physicists apply mathematics; does that make them applied mathematicians? I'm not certain.

On the other hand, while I find these sorts of theorems nice results, they do not change one bit of my understanding.

agree . the top theoretical physicists are effectively top mathematicians, too. Witten got a Fields Medal. you need to understanding algebraic geometry, topology, diff. geometry, diff. equations, numerical analysis, special functions, stats, etc. to be a top physicist. Pretty much everything is pure math.

Roger Penrose is a Professor of Mathematics, not Physics. It's not unusual for mathematicians to also be theoretical physicists.

Assume a hyperbolic paraboloid cow ...

Explanation of the joke: https://en.wikipedia.org/wiki/Spherical_cow

“If you perturb AdS space-time and wait a sufficient time,” Moschidis said, “you’ll end up with a different geometry — one that contains black holes — and it’s no longer AdS. That’s what we mean by unstable.”

But our universe is known to contain black holes and yet isn't it being AdS considered an open question ? Or is it only an open question about the universe during its infancy ?

Our universe is definitely not described by anti-de Sitter space. It might be de Sitter space though.

Then why do we care so much about AdS/CFT correspondance ?

The bulk-boundary equivalency. It seems it's possible to describe some models' insides just by studying its surface. (Hence the holographic principle.)

It seems to be an approach to study quantum gravity.

(Drive-by plug for Stochastic electrodynamics.)

> If the boundary is, in fact, reflective, nothing can leak out of AdS space-time. So any matter or energy put into the system could potentially get concentrated — perhaps to such an extent that a black hole would form.

So in space-time that does not have a reflective boundary, is the implication that matter or energy can leak out? Where does it go?

If my understanding is right, de Sitter space effectively has no boundary, in the same way that a sphere has no edge.

> The Stanford mathematician Jonathan Luk describes Moschidis’ work as “amazing. … What he’s discovered is a rather general instability mechanism” — one that could apply to other settings, unrelated to AdS, in which matter or energy is cooped up within a physical system that has no escape hatches.

So the I'm not particularly interested in the specific result, but the "rather general instability mechanism" is potentially game changing.

Does any know how general this mechanism is? Could it apply to Navier-Stokes?

Can someone expand on what this means for AdS/CFT?

When they mentioned "other settings, unrelated to AdS, in which matter or energy is cooped up within a physical system that has no escape hatches." I thought immediately of the fusion reactor I've been working on.

In my device, an arangement of static fields creates a region in which deuterium energised in a specific reflects back to the center forever and has no outlet even after non-fusion collisions.

The "instability" in my system comes because the extreme stability in the oscillation should cause even a rare event (DD fusion) to happen eventually with 100% probability.

Does this mean we're now sure that spacetime has positive curvature ( >= 0 ) ?

AdS has constant negative curvature. I don't think he proved that any spacetime with a negative curvature is unstable. But experimental data so far show that the universe has zero curvature.

Hey, are we emulsion floating on the surface tension of a still, multi-dimensional pond in which we all eventually sink? asking for a friend

Not necessarily. These three models are the simplest ones - and our universe has a much different matter distribution than any of the three.

It's still possible that adding more features to the solution, such as mass or angular momentum, changes the stability. It's also possible we do live in an inherently unstable universe, but even unstable things can have long periods of time elapse before breaking down.

It's mostly an interesting mathematical curiousity.

So my understanding is that the Maledecena conjecture that provide a correspondence between AntiDeSitter Space and CFT was a crucial breakthrough for proving string theory. Does this discovery make an impact on string theory?

> proving string theory

Would definitely not consider string theory “proven”.

On the contrary, its odds of being correct (much less demonstrably so) seem to be decreasing by the year.

I was under the impression that string theory was inherently un-provable.

Can anyone relate this to a human scale? What would it mean to be caught in an unstable space-time? How could it be exploited?

What is special about wave 2? Wouldn't 3...n behave the same way and result in stability?

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