Pedagoguery

I have written before about the fundamental dichotomy in modern physics: that between general relativity and quantum mechanics. This dichotomy affects a number of problems, none more fundamental than the beginning of the universe itself. Certain aspects of one of the leading quantum gravity theories, called loop quantum gravity, encourage us to take a close look at the details of the Big Bang in a new way.

One of the fundamental concepts introduced by loop quantum gravity is atoms of space. By this, the theory indicates that there is a limit to how small you can go, and consequently, how much energy a volume of space can contain. In general relativity, there is no such limit, allowing an infinite amount of energy to be packed into an infinitesimal space – a singularity. However, because of the finite limits in quantum loop gravity, such singularities are not possible, meaning something else existed at the time of the Big Bang. Viewed in this way, singularities in general relativity are evidence that the theory breaks down.

Loop quantum gravity emerged out of a two-step process. First, general relativity was reformulated to look like classical electromagnetism. The “loops” are the gravitational analog of electric and magnetic fields. Secondly, quantum principles were applied to the loops. The result was a view of spacetime made up of “atoms”, i.e. indivisible units of a fixed size. On large scales, the atoms mesh together so tightly that they appear to be a continuum, but at small scales, they behave quite differently.

When you pack energy into a volume of space, the wavelength of the particles carrying that energy has to shrink. Once the wavelength shrinks to the size of a spacetime atom, it can shrink no further. Any attempt to pack more energy into that space will result in it being pushed out. In effect, the local force of gravity becomes repulsive rather than attractive. This forms a key view of what potentially happened in the Big Bang. At that moment, the universe had a high but finite density, about as much as a trillion solar masses packed into every proton sized region. At that density, gravity was repulsive, thus causing the universe to expand. Initially, the expansion increased at an exponential rate, i.e. inflation, but as density decreased, that impetus was lost, and the excess energy was converted into matter. Thus, instead of being somewhat ad hoc in current theories, loop quantum gravity appears to build inflation right in.

In the classical view of the Big Bang, both time and space begin at that point. However, this is not true of the quantum view of the Big Bang. Given that the density of the universe was finite, it follows that the size of the universe was likewise finite, and thus spacetime did not begin at that point. This brings up an intriguing possibility of a time before the Big Bang. One possibility is a “Big Bounce”, a universe that collapsed under its own gravitational forces, until density became so high that gravity turned repulsive and resulted in the universe we see today. Could we then deduce what conditions were like in that prior universe? Unfortunately, current analysis seems to indicate that this is impossible. It is quite likely that the universe went through an extended period in a quantum state that scrambled all information about prior states of the universe. In fact, our universe could have arisen out of such a state without there having been a prior universe at all. However, this loss of prior information may actually be a good thing. For, if the prior information were retained, the entropy of the prior universe would also be retained, and it may not have been possible for complex structures like us to arise.

Next time, Enceladus.