Is Space Time a Lattice?

killerinstinct

It seems unlikely that space time is a lattice because it contradicts the fundamental assumptions and theories in physics. If space-time is a lattice
its dimensions are likely to be on the order of the Plank time and distance
scales. Opinions?

Mike2

Isn't a lattice oriented with respect to some points in an assumed coordinate system? Wouldn't a lattice therefore assume a continuous manifold with its coordinate system?

marcus

no actually, a lattice can be rigorously defined without using a coordinate system

no assumption of a continuous manifold need be made

Mike2

I'd like to see that.

marcus

there are various ideas of what a lattice is and some definitions do use coordinates! my point is that when some people say lattice they are talking about something that doesnt need coordinates

like Tulio Regge's famous 1961 paper "General Relativity without Coordinates"

that this guy referred to for instance:
Dr. Adrian P. Gentle, Los Alamos National Laboratory

"The application of Regge calculus, a lattice formulation of general relativity will be reviewed in the context of numerical relativity. The current state of numerical relativity will be briefly discussed, after which the lattice formulation of general relativity due to Regge will be introduced. Several illustrative examples will be examined, with particular emphasis on problems of astrophysical interest. Applications will include the construction of initial data for the head on collision of two black holes, and the time evolution of axisymmetric gravitational radiation."
http://www4.ncsu.edu/~lkn/math-physics-seminar/

Here is the Wolfram Scienceworld entry on Regge calculus
which has a dozen or so references (some online) in case you
want to pursue it

http://scienceworld.wolfram.com/phys...eCalculus.html

The simplicial lattice used by Regge calculus is essentially combinatorial: can be defined abstractly as a set of abstract points (which do not have to live in some manifold or euclidean space) which are connected to form (abstract) simplices.

I dont suppose Regge calculus is the only example, but it is one example and it looks like one of Regge's primary motives was to get away from having to use coordinates----kind of thing you asked about.

Mike2

The reference you gave states, "The approximation of Einstein's continuum theory of gravitation by a simplicial discretization of the metric space-time manifold". And an approximation of a continuum... still assumes a backgound continuum.

My objection is basically, how can information or a signal travel from one point in a lattice to another through ABSOLUTELY nothing, through disconnected points? Obviously, it can't. There must be something between points for signals to travel across.

Janitor

Another speculative model is that the universe is a cellular automata. But it has been pointed out that quantum correlations would not work in a deterministic automata.

marcus

hi Mike2, I am not talking about what you or someone says lattice is an approximation to
I said only that lattice can be defined without coordinates and without manifold.
You said "show me"


You said lattice needs a manifold to define it.
I said no, mathematically speaking it can be rigorously defined
without coords. Maybe a small technical point, but interesting to me.
You said show me, I'd like to see a case.
I have shown you a case.


However there is an interesting related question!!! can spacetime be modeled successfully with a lattice?
Is lattice "only" an approx, so you must let spacing go to zero in limit to get best approx. Or do you only make spacing so small (planck) and stop. becaause maybe then it actually fits better. Maybe you do not let spacing go in limit to zero. this would be like saying spacetime is "really" lattice, not manifold.

I mention this issue, although too speculative for me to want to discuss it, because You may want to discuss it with anyone who is interested.


To me, lattice and manifold are both merely mathematical gadgets and the modelbuilders use these gadgets to model physical events. And they work well or they work poorly.

One hears that in Quantum Field Theory they use lattices a lot, because it brings results. who knows, someday they may use the dynamical triangulations of Ambjorn and Loll and that might work even better
but for now I am not even going to guess.

Maybe it is something to discuss with the one who started the thread.

BTW when physicists use lattices and define fields on them and the fields undulate, the physicists are not bothered by the empty space in the lattice,
nor are the fields bothered by this. But you say that you are objecting to the holes in the lattice.

A field can live on the nodes of a lattice and influence can travel thru the lattice, even tho there are gaps. But you object to this, which is the mathematics of doing physics on a lattice. It is a time-honored practical thing. Probably basic to the Standard Model and QFT and all that. I am not explaining the Standard Model or QFT, so it is not my place to argue.

Mike2

It would seem my objection remains. If space and/or time is discrete, then how can a signal propagate through either no medium at all, or through discontinuities? Perhaps this is the same question as: how can a disturbance propagate through a continuous field without dispersing in all direction as is done in classical waves? In other words, what is the nature of a quantum field such that particles maintain there characteristics without spontaneously dispersing like a classical wave?