Rethinking Einstein: The end of space-time

Physicists struggling to reconcile gravity with quantum mechanics have hailed a theory – inspired by pencil lead – that could make it all very simple

IT WAS a speech that changed the way we think of space and time. The year was 1908, and the German mathematician Hermann Minkowski had been trying to make sense of Albert Einstein's hot new idea - what we now know as special relativity - describing how things shrink as they move faster and time becomes distorted. "Henceforth space by itself and time by itself are doomed to fade into the mere shadows," Minkowski proclaimed, "and only a union of the two will preserve an independent reality."

And so space-time - the malleable fabric whose geometry can be changed by the gravity of stars, planets and matter - was born. It is a concept that has served us well, but if physicist Petr Horava is right, it may be no more than a mirage. Horava, who is at the University of California, Berkeley, wants to rip this fabric apart and set time and space free from one another in order to come up with a unified theory that reconciles the disparate worlds of quantum mechanics and gravity - one the most pressing challenges to modern physics.

Since Horava published his work in January 2009, it has received an astonishing amount of attention. Already, more than 250 papers have been written about it. Some researchers have started using it to explain away the twin cosmological mysteries of dark matter and dark energy. Others are finding that black holes might not behave as we thought. If Horava's idea is right, it could forever change our conception of space and time and lead us to a "theory of everything", applicable to all matter and the forces that act on...

It really is not whimsical. What Petr did in his initial paper is justified, and, in retrospect, it is suprising that none of us thought of doing it earlier. It is not really possible to go into the full details of this in a forum such as a blog, but the main point is that, at “finite temperature” (this the jargon we use to refer to physical systems at temperatures above zero), Lorentz invariance (”Lorentz symmetry,” as it is referred to in the article) is automatically violated. The reason is that the mere statement that there is a finite temperature at all implies that there is present in the problem a large number of particles in the “background” that together make up what is referred to as a “heat bath.” The word “temperature” actually refers to a statistical measure associated to this background heat bath. However, this is the reason that Lorentz invariance is broken: the aggregate properties of the large number of particles that, together, make up the heat bath, among many other things, implicitly pick out a so-called “preferred direction” in spacetime. This “preferred direction” (technically, this is the direction in spacetme towards which the velocity 4-vector of the heat bath points) intrinsically breaks Lorentz invariance. What Petr did in his paper is technically justified. Other physicists later showed (as described in the article) that the original paper didn’t properly reduce to general realtivity (whcih DOES exhibit Lorent invariance) at low temperatures, but that defect of the original Horava idea has since been fixed. This is all still very much research in progress.

Thanks for the explanation.

My pleasure.

“E8” — I’ve seen that before! (Lisi)

The "E8" in my name refers to a so-called "Lie group," a type of mathematical structure that plays an important role in the physics of elementary particles (Lie groups have many other uses in other fields, as well). "E8 cross E8" refers to what is called the ("semi-direct") tensor product of two copies of this Lie group - this product of groups has played a crucial role in string theory. My use of this as a name is in this context.

I should point out that this article, as is the case with far too many popular science articles, has various misleading and inaccurate statements. To wit:

And so space-time - the malleable fabric whose geometry can be changed by the gravity of stars, planets and matter - was born. It is a concept that has served us well, but if physicist Petr Horava is right, it may be no more than a mirage.

This is astoundingly wrong. Petr's work implies no such thing. His explicit calculations simply take account of the fact that, based on an assumption that there was a very high average temperature in the early universe, Lorentz invariance is violated at finite temperature. As a result, he makes use of a set of techniques that are together called "finite temperature quantum field theory," in which Lorentz invariance is violated, rather than zero temperature quantum field theory, in which Lorentz invariance is not violated. (Both finite- and zero-temperature QFT are very well known. The fact that Lorentz invariance is broken in finite temperature QFT is also very well known. Basically (oversimplifying things a bit), the new idea was to apply this method to the explicit calculation of interactions involving gravitons in the early universe.) There is certainly no notion, quantitatively or qualitatively, either in the original Horava paper or in any of the subsequent papers that cite it, of spacetime being a "mirage." The author of the popular article should have had his article vetted by a physicist prior to releasing the final copy. (Petr Horava would never have put things the way the author of the popular article did.)

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