Axion Experiments to Algebraic Geometry: Testing Quantum Gravity via the Weak Gravity ConjectureThey hash out a refinement of our conjecture that for whatever type of a "charge" like to electromagnetism, in that location must ever be sources for which the non-gravitational forcefulness donalds the gravitational one.
The essay shows that the inequality has implications for inflation (naively excluding a long plenty inflation in addition to possibly forcing i to verbalize close specific types of inflation), for AdS/CFT (charged operators alongside depression plenty dimensions should exist), in addition to for pure mathematics (because the inequality should handgrip for compactifications on complicated plenty manifolds, in addition to such an inequality thus sometimes turns into a nontrivial geometric theorem close those).
They start alongside my #1 favorite motivation for the weak gravity conjecture – the absence of global Lie symmetries inwards quantum gravity. It's been something I was emphasizing long earlier our newspaper but I vaguely retrieve that it wasn't novel for to a greater extent than or less or several co-authors, either.
You know, the of import pre-WGC lore – which I may receive got known from my adviser Tom Banks since the belatedly 1990s – was that in that location are no global continuous symmetries inwards a consistent quantum theory of gravity. In full general relativity, fifty-fifty translations are made "local" (diffeomorphism group) in addition to things that are non "local" croak unnatural.
However, gauge theories alongside tiny couplings \(g\to 0\) may seemingly emulate global symmetries every bit accurately every bit you lot want. That should ameliorate last impossible every bit well. If something (global symmetries) is forbidden, physical situations or vacua that are "infinitesimally close" to the forbidden thing should ameliorate last banned every bit well, right? Otherwise the ban would last operationally vacuous. There should be a finite value of to a greater extent than or less quantity that tells you lot how far from the forbidden betoken you lot receive got to be.
And that's what the weak gravity conjecture does (and many types of show – from problems alongside extremal dark hole remnants to lots of stringy examples – back upwards the conjecture, at to the lowest degree inwards "some" form). Influenza A virus subtype H5N1 low-cal charged particle alongside \[
m \leq \sqrt{2} eq M_{Planck}
\] must exist. Heidenreich et al. promote their belief inwards a stronger "detailed" version of the weak gravity conjecture that nosotros receive got conjectured but nosotros ran into to a greater extent than or less counter-arguments. They telephone telephone it the lattice weak gravity conjecture (LWGC): for every allowed vector \(\vec Q\) inwards the lattice of charges, in that location must be an object that is lighter than the 0.0001% of the volume of a dark hole alongside the accuse i 1000000 times \(\vec Q\).
(I receive got inserted the factor of i 1000000 in addition to the millionth to brand sure that you lot omit the corrections from the smallness of the dark hole – you lot operate alongside the semiclassical justice of the mass.)
This sounds also strong. I idea that for larger charges, the declaration really isn't truthful – exclusively several "elementary", low-charge low-cal particles are required yesteryear WGC, I thought. If they replaced the give-and-take "particle" yesteryear a "state" (which may last a collection of many split particles whose charges, masses add), I think that my doubts would croak away.
It's hard to attain upwards one's heed whether the novel low-cal states should be for every \(\vec Q\), every management inwards the accuse space, almost every direction, every management inwards a footing of directions, every management inwards a (near) orthogonal footing inwards to a greater extent than or less metric, or something else. There may be to a greater extent than or less "very natural" specific version of the inequality that would last every bit provable every bit e.g. the Heisenberg uncertainty regulation but I don't think that the "best, most accurate yet potent one" has been pinpointed yet.
The analogy alongside the Heisenberg uncertainty regulation is meant to last an exaggeration. At to the lowest degree I nonetheless believe that the WGC is vastly less key than the Heisenberg uncertainty principle. The uncertainty regulation may last connected to many – inwards to a greater extent than or less feel "all" – situations inwards physics. WGC has been "connected" to many things. But I nonetheless don't run across inwards what feel it could last considered a regulation that "changes the rules of the game" inwards a means that is at to the lowest degree qualitatively analogous to the alter of physics implied yesteryear the Heisenberg uncertainty principle.
There may last similarities betwixt the inequalities but in that location are also differences. One of them is that the Heisenberg uncertainty regulation strictly disagreed alongside the shape of theories that had been considered earlier Heisenberg in addition to pals revolutionized physics. On the other hand, WGC tells you lot to consider a subset of the theories of gravity-coupled-to-matter that were previously allowed.
The amount of action dedicated to WGC is greater than what I used to assume a decade ago. (And I sure believe that e.g. matrix string theory is much to a greater extent than fundamentally of import than WGC, for example.) On the other hand, I can imagine that this work of enquiry on WGC volition plough into something that volition last self-evidently key inwards its implications.
As nosotros said at the beginning, WGC talks close to a greater extent than or less "minimal departure betwixt 2 situations" – also decoupled novel forces (with also weak couplings and/or also heavy charged particles) are forbidden etc. So this WGC-dictated "minimum distance" could last a termination of to a greater extent than or less novel sort of "orthogonality" that is indeed analogous to (if non a special instance of) the orthogonality of mutually exclusive states inwards quantum mechanics – which is an supposition that may last used to derive the uncertainty principle.
By maxim that the lightest accuse particles receive got to last low-cal enough, the WGC also quantifies the intuition that all the "engines" responsible for a forcefulness etc. tin never last squeezed into a also modest percentage of space. You ask the rather long distances – the Compton wavelength of the low-cal plenty particle – for this forcefulness to arise. That's a means to say that WGC may last said to last "somewhat similar" to the holographic principle, too. All these things advise that the data can't shroud inwards also modest volumes, or inwards also inaccessible physical phenomena.
If something seems to last nontrivially right – it doesn't look to last quite a coincidence that gravity is the weakest forcefulness – the reasons should ameliorate last understood well. So people's thinking close it is clearly desirable. On the other hand, no i is guaranteed that it volition Pb to a full-fledged revolution. If WGC really implied that no model of inflation may exist, I would personally non believe such a conclusion, anyway (except if someone gave me a genuinely convincing total Definition of quantum gravity alongside all the proofs; or at to the lowest degree to a greater extent than or less feasible option to inflation). Maybe it's a error of mine but I nonetheless plough over to think that the "case of inflation" is nonetheless much stronger than the "case for whatever especial potent version of WGC applied to instantons". (Whether the inequality for 1-forms may really last applied to 0-forms seems disputable to me, too. Note that the energy-time "uncertainty principle" must last interpreted differently, if it is possible at all, than the momentum-position uncertainty principle, in addition to i must oft last real careful when he generalizes things to "related situations".)
The subtitle "Testing Quantum Gravity via the Weak Gravity Conjecture" must last provocative for assorted Šmoits. Not exclusively the essay dares to verbalize close the testing of quantum gravity. It's worse than that: quantum gravity in addition to string theory are beingness tested according to a conjecture co-authored yesteryear a guy who insists that Šmoits in addition to their apologists are simply stinky piles of feces. ;-)
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