Biggest neutron star

I've just finished a book by Carlo Rovelli called Reality Is Not What It Seems, tremendously well written and for a general audience. He speaks of the Loop Quantum Gravity ( LQG ) attempts that have been made in recent years. It's not a competitor to String Theory, which aims at force unification, but a direct throw at literally quantizing spacetime. LQG tries to meld Quantum Field Theory with General Relativity, and may accidentally unify as a side effect.

The logic is roughly as follows : the primary foundation of reality is fields of all sorts, fields are assumed as basic elements without other justification, thus the gravitational field is one of them, hence to quantize this field is to quantize space & time. This places a lower limit on the size of a volume of space and a tick of time. The scale at which this exists is incredibly small, you start with the Planck length ~ 10^{-thirtysomething} metres^*, that being the size of the event horizon for a particle becoming a teensy weensy black hole. In other words one can't probe ( read : measure ) any smaller distance because particles can't come any closer without disappearing. Thus the minimal spatial volume becomes ~ 10^-hundredish metres³. LQG claims that nothing exists below that scale. All fields lie one upon another as it were. An excitation of spacetime becomes the graviton, similar to an excitation ( read : resonance ) of the electromagnetic field being a photon.

The loop bit comes in by tracing paths that go around spacetime in, well, a loop ( the starting point is the end point of some traversal ). In the theory the minimal volumes are modelled as nodes which are connected via adjacent common areas. One could visualise this as all manner of polyhedra squeezed together cheek by jowl. Spin enters the discussion here for reasons I didn't quite catch, but anyway it is possible to parallel transport a spin vector around a loop and hence deduce any curvature of spacetime if said vector doesn't point in the same direction as when it started. This curvature is the very same that Einstein's General Relativity speaks of. Hence we have satisfied Quantum Mechanics and GR. GR is the higher scale approximation to LQG. Plus with a minimum volume restriction you sneak out of the singularity/infinity problems of classical GR : numbers can be horrendously large but still finite. Maximum density for a black hole anyone ? :-0

The really anti-intuitive bit is ( of course there's a price to pay ) that to be truly-rooly consistent with QM then one must accept that probability comes into the description of spacetime structure. Down at the Planck length all possible structures act like superposed QM states with complex amplitudes, and thus need to be integrated^** ( by Feynman's sum over histories or lattice approximations ) to yield the most probable actual structure if measured ( read : probed ).

But it is a work in progress and much remains to be figured out. The good news is that if successful they expect to be able to produce testable numbers ie. confront the theory with observation. Unlike String Theory which has left the tent flap open and has gone AWOL in a blizzard of mathematics.

Cheers, Mike.

* The Planck time is 10^{-fortysomething} of a second : the time taken for light to travel the Planck length. I put that in to be complete, but that's a hard ask to conceptualise such a short interval. I have enough trouble with the 10^{-twentysomething} that LIGO measures.

** This introduces the issue of boundary conditions, what 'really' happened within some time interval and like quantum conundrums. It's hard to accept I think that a definite ordering of events is a luxury of our human scale. Specifically down at the spacetime foam, as it is called, cause and effect are somewhat blurred. One is left with the idea that some of the contributing states are specifying that things may occur out of causal order, but as long as the state meets given boundary conditions then it may contribute to a summation. In fact it is actually hard to put this aspect into normal language, which is a product of our scale of reference.

At a classical scale this is reminiscent of out of order execution of computer code : take two tasks that can be done in either order, but in the program code one will be written as sequentially before the other. Now imagine that one task knows the result of the other before it is done. It's something like that. Weird.