I steal the title of Lee Smolin's new review paper, pub­lished on Arxiv last Fri­day, as the titile of this post. Here is the link of his paper: http://​www​.arxiv​.org/​h​e​p​-​t​h​/​0​6​0​5​052. In this paper, he sum­ma­rized and dis­cussed seven generic pre­dic­tions of a group of quan­tum the­ory of gravity—the so-called causal spin net­work the­o­ries. Here is his list of predictions:

1. Dis­crete­ness of quan­tum geom­e­try and ultra­vi­o­let finite­ness
2. Elim­i­na­tion of space­time sin­gu­lar­i­ties
3. Entropy of black hole and cos­mo­log­i­cal hori­zons
4. Pos­i­tive cos­mo­log­i­cal con­stant space­times are hot.
5. Deformed spe­cial rel­a­tiv­ity
6. The emer­gence of mat­ter from quan­tum geom­e­try
7. Dis­or­dered local­ity

In Smolin's words, the first four are well estab­lished ones, the 5^th is the sub­ject of recent progress and the last two are new. He dis­cussed the 5^th one and exper­i­ments would be able to fal­sify it in an ear­lier paper: Fal­si­fi­able pre­dic­tions from semi­clas­si­cal quan­tum grav­ity. Here is the abstract:

Quan­tum grav­ity is stud­ied in a semi­clas­si­cal approx­i­ma­tion and it is found that to first order in the Planck length the effect of quan­tum grav­ity is to make the low energy effec­tive space­time met­ric energy depen­dent. The dif­feo­mor­phism invari­ance of the semi­clas­si­cal the­ory for­bids the appear­ance of a pre­ferred frame of ref­er­ence, con­se­quently the local sym­me­try of this energy-dependent effec­tive met­ric is a non-linear real­iza­tion of the Lorentz trans­for­ma­tions, which ren­ders the Planck energy observer inde­pen­dent. This gives a form of deformed or dou­bly spe­cial rel­a­tiv­ity (DSR), pre­vi­ously explored with Magueijo, called the rain­bow met­ric. The gen­eral argu­ment deter­mines the sign, but not the exact coef­fi­cient of the effect. But it applies in all dimen­sions with and with­out super­sym­me­try, and is, at least to lead­ing order, uni­ver­sal for all mat­ter cou­plings.
A con­se­quence of DSR real­ized with an energy depen­dent effec­tive met­ric is a helic­ity inde­pen­dent energy depen­dence in the speed of light to first order in the Planck length. How­ever, thresh­olds for Tev pho­tons and GZK pro­tons are unchanged from spe­cial rel­a­tivis­tic pre­dic­tions. These pre­dic­tions of quan­tum grav­ity are fal­si­fi­able by the upcom­ing AUGER and GLAST experiments.

These remind me a recent paper by Jacques Dis­tler: Fal­si­fy­ing String The­ory Through WW Scat­ter­ing, in which he also claimed fal­si­fi­able pre­dic­tions of string the­ory. Here is his abstract:

We show that the coef­fi­cients of oper­a­tors in the elec­troweak chi­ral Lagrangian can be bounded if the under­ly­ing the­ory obeys the usual assump­tions of Lorentz invari­ance, ana­lyt­ic­ity and uni­tar­ity for all scales. Vio­la­tions of these bounds can be explained by either the exis­tence of new physics below the naïve cut-off of the the effec­tive the­ory, or by the break­down of one of these assump­tions in the short dis­tance the­ory. If no light res­o­nances are found, then a mea­sured vio­la­tion of the bound would fal­sify string theory.

You can find some use­ful dis­cus­sions of Distler's paper here: http://​www​.physics​fo​rums​.com/​s​h​o​w​t​h​r​e​a​d​.​p​h​p​?​t​=​1​1​9​368 and here: http://www.math.columbia.edu/~woit/wordpress/?p=385.

These are very nice papers that help you to obtain an overview of how these the­o­ries are con­nected to the real world.

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