Slicing Through the Gordian Knot of Quantum Gravity: Alternatives to String Theory (Part 3 of 3)

Quantum mechanics is the physics of the smallest of things, while general relativity is the physics of the largest. Not surprisingly, many physicists have been obsessessed with finding a Theory of Everything (TOE) that encompasses both limits.

This has not been easy.

In previous posts I’ve written of the difficulties that arise in creating a coherent theory of quantum gravity, and how one popular approach, string theory, attempts to solve the problem. String theory is not a failure, but neither has it been the overwhelming success quantum mechanics and general relativity have been. In particular, string theory has in general failed to make verified predictions in fundamental particle physics. (NB: some of the mathematical techniques of string theory have been applied to other areas of physics, but this is not the same thing.)


One useful way to verify a theory is to look at the different predictions they make and see which match up better to experiment. There are, for example, alternatives to general relativity and quantum mechanics, and experimentally the orthodox theories have won hands down.
In this post I’ll write about a couple of recent alternative approaches to quantum gravity that have stirred considerable interest over the past year.

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One of the great innovations of Isaac Newton was to assume that the laws of motion were universal: the same laws applied to an apple falling to the ground in an orchard as to the moon in orbit about the Earth. This contrasted to Aristotle who, brilliant thinker and observer that he was, conceived of the universe as a hierarchy, with the terrestrial globe corrupt and changeable while the celestial sphere was perfect and unchanging.

Einstein took this a step further, and assumed that time and space could and should be treated on an equal footing (a concept anticipated by the Time Traveler in H.G. Wells’ The Time Machine). While a wacky idea, it has experimentally verified consequences, such as time dilation for particles traveling close to the speed of light, and nuclear bombs.Mathematically, this has become known as Lorentz invariance, after the Dutch physicist who first invented a kind of transformation between space and time (although he only thought it a mathematical trick; Einstein took it as being real).

Paul Dirac incorporated Lorentz invariance into quantum mechanics, and his eponymous wave equation predicted the existence of antimatter and that electrons have intrinsic spin, both experimentally verified.

So far so good. Alas, when you go further, and incorporate the supple geometry of general relativity and the flickering existence of matter-antimatter pairs from quantum field theory, the mathematics literally blows up.

If you conduct an autopsy on the integrals–and I’m sure you all do this kind of thing regularly, as a hobby–you find that Lorentz invariance, that is, equal weighting of space and time, was deadly.

In 2009, Berkeley mathematical physicist Petr Horava suggested breaking Lorentz invariance, that is, not treating space and time as equal, thereby curing the exploding integrals (or at least making them amenable to standard treatments in quantum field theory).

Of course, we’ve tested Lorentz invariance, and continue to test Lorentz invariance. But any such test has to be performed on a particular length scale. Horava suggested that Lorentz invariance only breaks down on very small length scales that have not yet been tested, but that it does work on larger, human-sized length scales.

Horava’s original paper had a number of technical problems, but was intriguing enough to inspire a huge number of follow-on papers in a very short period of time. It still remains to be seen what exact experimental consequences come out of Horava gravity (also called Horava-Lifshitz gravity).

One possible sfnal consequence is that if Lorentz invariance is broken on some scale, the speed of light may not be quite as iron clad as thought. Maybe one can’t send ships faster than light, but messages…? This is highly speculative, of course, but wild speculation is the bread and butter of science fiction authors.

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Part of the problem of quantum gravity is that gravity is unlike all other fundamental forces. Electromagnetism and the weak and strong nuclear forces, although superficially very different, are all vector forces. This is mathematical shorthand for how one writes down the equations, but one consequences that one has both positive and negative charges. Gravity, however, is a tensor force, and has only “positive” mass. (It is possible to conceive of “negative” energy density, and indeed this is required to make a wormhole, but some unproven theorems of gravity suggest negative energy densities are impossible.)

Gravity is so different from fundamental forces, in fact, that in the 1960s the Soviet physicist and dissident Andrei Sakharov wondered if gravity was not a fundamental force at all, but rather an “emergent force.” We are familiar with these kinds of forces: the elastic force in a spring, for example, is very simple even though it emerges from averaging over complicated interatomic interactions.

Though Sakharov’s suggestion was appealing, it was nothing more than a slogan until 1995, when a paper by Ted Jacobson showed how one could derive general relativity from a thermodynamic framework.
While at first glance the idea of a thermodynamic origin for gravity sounds crazy (but when you are desperate, you cling to crazy ideas), at second glance it’s not so bad. In the 1970s Bekenstein and Hawking showed that black holes follow simple, thermodynamic relationships: that black holes have an entropy and a temperature, that depends upon the area of the event horizon. Hawking’s famed radiation from black holes is a natural consequence of this thermodynamics.
What Jacobson, and later Erik Verlinde also in 2009, did was to turn this inside out: they considered a horizon around any observer and treated this horizon as a black hole. To repeat a familiar refrain, this is not as crazy as it first sounds: since an arbitrary horizon will, actually, absorb any radiation passing through it, it acts just like a blackbody absorber–or like a black hole.
This neatly solves the problem of quantum gravity by eliminating gravity at the microscopic scale–gravity is emergent and macroscopic and there is not need for a quantum theory of gravity.

This, too, has inspired many other papers. There are two problems. First, it is not at all clear what testable experimental results there are, aside from the complete absence of quantum gravity (a difficult thing to observe). Second, exactly what is thermodynamic is unclear, but it might be the boiling soup of the vacuum.

And as you probably figured out, the latter might be the solution to the former: affect somehow (invoke sfnal device here) the quantum vaccuum, and you might affect gravity. And voila, there’s your star drive.

I admit to finding emergent gravity particularly appealing, but the likelihood of either of these providing the solution to quantum gravity is small…but then, the very fact that such wild suggestions prove wildly popular suggest just how frustrated physicists are with string theory as a Theory of Everything.

Many of these papers and others can be found for free at arxiv.org, a repository of preprints for physics, mathematics, and other sciences.

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