In an attempt to better understand spacetime, mathematical physicist Achim Kempf of the University of Waterloo has proposed a new possible structure of spacetime on the Planck scale. He suggests that spacetime could be both discrete and continuous at the same time, conceivably satisfying general relativity and quantum field theories simultaneously. Kempf’s proposal is inspired by information theory, since information can also be simultaneously discrete and continuous. His study is published in a recent issue of *Physical Review Letters*.

“There are fiercely competing schools of thought, each with good arguments, about whether spacetime is fundamentally discrete (as, for example, in spin foam models) or continuous (as, for example, in string theory),” Kempf told *PhysOrg.com*. “The new information-theoretic approach could enable one to build conceptual as well as mathematical bridges between these two schools of thought.”

As Kempf explains, the underlying mathematical structure of information theory in this framework is sampling theory - that is, samples taken at a generic discrete set of points can be used to reconstruct the shape of the information (or spacetime) everywhere down to a specific cutoff point. In the case of spacetime, that cutoff would be the natural ultraviolet lower bound, if it exists. This lower bound can also be thought of as a minimum length uncertainty principle, beyond which structural properties cannot be precisely known.

In his study, Kempf develops a sampling theory that can be generalized to apply to spacetime. He shows that a finite density of sample points obtained throughout spacetime’s structure can provide scientists with the shape of spacetime from large length scales all the way down to the natural ultraviolet cutoff. Further, he shows that this expression establishes an equivalence between discrete and continuous representations of spacetimes. As such, the new framework for the sampling and reconstruction of spacetime could be used in various approaches to quantum gravity by giving discrete structures a continuous representation.

“It is exceedingly hard to obtain experimental data that could guide the search for the theory that unifies quantum theory and general relativity,” Kempf said. “The proposal that spacetime is simultaneously continuous and discrete in the same way that information is may be able to serve as a theoretical guiding principle. It points towards a theory in which all natural processes are seen as possessing what is in effect a universal finite bandwidth.”

Kempf added that, at the very least, the new approach provides some practical technical tools for studies in quantum gravity, such as solving discrete problems and using continuum methods. In the future, Kempf plans to apply the new methods to a variety of problems.

“I am planning to use the new information-theoretic methods to tackle afresh certain long-standing information-theoretic questions in quantum gravity, such as the black hole information loss paradox and the question of the role of the holographic principle in quantum field theory,” Kempf said.

**Explore further:**
Generally Speaking: A Primer on General Relativity

**More information:**
Achim Kempf. “Information-Theoretic Natural Ultraviolet Cutoff for Spacetime.” *Physical Review Letters* 103, 231301 (2009).

## SincerelyTwo

Unified Theory = Continuous ^ Discrete.

The statement is true simply based on the conditions that satisfy either.

Usually when two sides of an argument can state a barrage of facts that cannot be disputed within 'their context' but can in another, it's indicative that the system, or problem, simply DOES have multiple solutions.

Why did it take so long for physicist to consider this publicly? Going so deep in to complex mathematics that you ignore basic logic?

I know i'm being vague, common, the char limit on these comments is like... 600 characters or something. If it makes sense to you then alright, otherwise, fukit.

## danman5000

Indeed. This reminds me of how light can act as either a particle or a wave depending on what experiment you do. Neither interpretation is really "right", and you have to consider it as being both forms simultaneously. Pretty interesting stuff.

## StillWind

I can't think of a better example than the illustration that accompanies this article. This is clearly wrong, since the gravity well of Earth is not centered "beneath" the south pole, but must ultimately resemble some form of torus that extends within the structure of the Earth.

Even, and maybe especially smart people are really just too limited in their ability to conceive the non-visible structure of space.

## googleplex

Agreed. They have barstewardized the 2d gravity well diagram by adding a 3d earth. The earth should be a 2d slice. Sadly it is impossible for us to visualize 4 dimensions (3d+t) bending.

For more information http://en.wikiped...nal_well

## googleplex

The current physics doctrine is that photons are fundamental and cannot be broken down into smaller units. So acceptance of the photonic dipole would require a doctrinal shift in physics.

## brant

Its because we cant see the real explanation(yet).

The 5 wise men and the elephant story would fit here.

## Dr_Mabuse

## joefarah

Perhaps we can extend that same model to space. The discrete component is more on the lines of the fact that Neutrons/Protons are extremely dense and so probably act as tiny black holes at sub atomic level. This would tend to make space more discrete when matter is near by. Now apart from matter (and hence energy) does it make sense to ask if space is discrete, especially if the presence of matter reshapes the space around it? Sort of like the tree falling in a forest when no one is around to hear it.

Just some thoughts.

## flaredone

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## exequus

I have a problem with the statement 'All matter is photonic.' For if current orthodoxy holds that photons are fundamental and therefore indivisible then it follows that if it's true that all matter is photonic it must of necessity be fundamental and therefore indivisible. But this is inconsistent with the generally accepted view of matter as made up of coalescing energy exchanges

between some twenty-something subatomic particles,

as explained by Gerard 't Hooft in his personal memoir of time spent 'In search of the Ultimate Building Blocks.' If all matter were found to be photonic it'd put a lot of people out of work at Fermilab and the LHC premises in Switzerland, all those folks who're working overtime smashing protons, counting leptons and baryons and crunching terabytes of raw data.

## baudrunner

Reality bytes.

## baudrunner

## baudrunner

It should be noted that those "space bosons" to which I give reference above in what is essentially a theoretical model of space-time are neither force-carriers nor matter particles, but rather in a class all by themselves. They are so small as to exceed only slightly the Planck length and the only recognizable characteristic which they possess is what amounts to a dipole moment.

## DreamWvr