Why Spacetime On The Tiniest Scale May Be 2-Dimensional

Wednesday, September 08, 2010

Why Spacetime On The Tiniest Scale May Be 2-Dimensional

The latest thinking about quantum gravity suggests that spacetime is 2-dimensional on the smallest scale. And there may be a way to prove it

In 1973, George Ellis and Stephen Hawking published a book called The Large Scale Structure of Spacetime. Their aim, they said, was to understand spacetime on the scale ranging from 10^(-13)cm to 10^28cm or, in other words, from the size of elementary particles to the radius of the universe.

That may sound ambitious but nearly 40 years later cosmologists have pretty much nailed it, says Steve Carlip, a theoretical physicist at the University of California, Davis. "To the best of our ability to measure such a thing, it behaves as a smooth (3+1)-dimensional Riemannian manifold."

Which is why theoretical physicists have turned their attention to the structure of spacetime on even smaller scales. However, there is a problem here. "For the most part we have neither direct observations nor a generally accepted theoretical framework for describing the very small-scale structure of spacetime," says Carlip. Indeed, nobody is quite sure whether the terms 'space' and 'time' have any reasonable meaning at this scale.

Today, Carlip outlines his own fascinating take on the problem which is that spacetime on the tiniest scale may be two dimensional. While that may seem a little counterintuitive, he says there is a growing number of indicators (evidence is too strong a word) that point to that conclusion.

Carlip says recent work in loop quantum gravity, high temperature string theory, renormalization group analysis applied to general relativity and other areas of quantum gravity research, all hints at a two dimensional spacetime on the smallest scale. In most of these cases, the number of dimensions simply collapse in a process called spontaneous dimensional reduction as the scale reduces.

One obvious question is that if only two dimensions are present on this scale, which two are they? Carlip calculates that they must be one of time and one of space. "At each point, the dynamics picks out a "preferred" spatial direction, leading to approximately (1+1)-dimensional local physics," he says.

He then moves into interesting territory with the claim that this preferred direction must be determined classically and then randomised by the physical processes at work on these scales. That sounds tantalisingly like a hidden variable theory of the kind that might please at least one Nobel prize-winning physicist.

The million dollar question is whether Carlip's take on the topic is correct. He cheerfully admits that the idea is "still very speculative". That doesn't distinguish it in any significant way from much of the rest of modern cosmology.

However, unlike many quantum gravity theorists, Carlip hints at the kind of experiments that might prove him right. "The process I have described breaks Lorentz invariance at the Planck scale, and even small violations at that scale can be magnified and lead to observable effects at large scales," he says.

That's an interesting thought. What he's saying is that the laws of physics at this scale ought to change according to the direction in which you're travelling. And although they'll constantly vary in a random way, that could still be measurable in a sufficiently clever experiment.

Time for the experimentalists to get to get their thinking caps on.

Ref: The Small Scale Structure of Spacetime




Carlip has written some OK papers about the black holes and other things but this paper is just a pile of nonsense.

In string theory, indeed, the entropy - according to the counting of states in all the well understood examples - is ultimately reduced to the 1+1-dimensional black holes. But that's just a mathematical transformation that leads us to an integrable system. Two-dimensional conformal field theories are well understood, especially their entropy, so if you manage to transform your system into the 2D CFT, you may say many things about the number of states. Because all the notions of locality may get completely distorted and lost, the possibility of this transformation surely doesn't mean that there's any useful reduction of spacetime's dimensionality. In particular, it doesn't mean that "dynamics chooses a privileged 1 spatial dimension".

The statement that such dynamics should be "classical" is even more nonsensical because all the calculation of the entropy is only possible if all the postulates of quantum mechanics are fully taken into account. Classically, there can't be any finite temperature or entropy of black holes etc. Moreover, statements that there is any classical physics underlying quantum mechanics may be disproved in a completely general setting, not just in quantum gravity.

It's even more nonsensical to build on string theory in combination with inconsistent would-be theories such as loop quantum gravity. Even if I am extremely conservative in these statements, loop quantum gravity is incompatible with string theory. So how its (irrelevant) statements can be used in combination with string theory? It's like saying that because 2+2=4 and also because 2+2 may be 5, it all suggests that 4+7 = 2.

More generally, Steve Carlip doesn't understand that the "Hilbert space itself" is not measurable. How we parameterize it is up to us. It's not yet about dynamics. Infinite-dimensional Hilbert spaces are all unitarily equivalent to each other. There's no information about the detailed laws of physics in them.

To determine dynamical questions, i.e. whether the space becomes 2-dimensional in any sense, one needs to study genuinely physical observables such as the S-matrix. Obviously, if the S-matrix or asymptotic Green's functions or any asymptotic observable of this kind is a starting point, we can't see any "reduction of the dimensionality of the bulk".

Also, according to the holographic principle - which is the only "universal" modification of spacetime dimensionalities in all consistent quantum gravity backgrounds - the spacetime dimension is not 1+1 but rather (D-2)+1 where D is the perceived dimension: one dimension gets eliminated. The statement that all of them get eliminated is just a misunderstanding what happens in holography.

I could go on and on and on. This is the typical pseudoscience that is completely incapable to separate myths, superstitions, prejudices, and wishful thinking from insights that are actually supported by rational evidence.
Flawed Concepts Are Hard to Kill

I am hoping that some day soon, the physics community will wake up out of its collective stupor and realize that their antiquated concepts of time and space don't have a leg to stand on. This is not because of some complex and convoluted reason that only a rocket scientist could understand. It is trivially easy to show that, contrary to Einstein's cheerleaders, a time dimension makes motion impossible. This is the reason that nothing can move in spacetime and that Karl Popper called spacetime, "Einstein's block universe in which nothing happens" (source: Conjectures and Refutations). It boggles my mind that Stephen Hawking, one of the most celebrated physicists in modern times can get away with saying that general relativity does not forbid time travel. It's rather annoying, to say the least. I mean, do these guys really understand the very theory they are supposed to be experts in? I have my doubts. Every physicist in the world should recite these words every day: Absolute nothing can move in spacetime. Hopefully, it will sink in.

"To the best of our ability to measure such a thing, it behaves as a smooth (3+1)-dimensional Riemannian manifold."

Oh yeah. What's with the concept of continuity in this day and age anyway? When will that nonsense go away? Should it not be obvious by now that continuity is not just illogical (it leads to an infinite regress), but it is not even scientific in the Popperian sense of falsification since it cannot be falsified by definition. When was the last time someone devised an experiment to disprove continuity? I mean, it doesn't pay to get too judgmental against psychics, religionists and astrologers for having faith when you're guilty of the same sin. In other words, don't throw rocks when you live in a glass house.

Last, but not least, what can one say about the space concept? Well, space (distance or volume), too, is utter nonsense. It is so easy to show that space is a perceptual illusion that children will have no trouble grasping it once it is explained to them. Folks, space is an abstract concept of the mind that the brain uses to make sense out of reality. It does not exist. Only particles, their properties and their interactions exist. Particles do not have a position in space. Position is just an intrinsic property of a particle, like mass and spin. Soon, physicists will kick themselves for having been so blind for so long.

It's time for the physics community to wake up and abandon the failed and bankrupt ideas of the last century. Otherwise, they won't know what hit them when the next revolution comes roaring by like a hurricane and make them obsolete overnight.


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