Pedro G. Ferreira

“My suspicion is that if the twentieth century was the century of quantum physics, the twenty-first will give full play to Einstein’s general theory of relativity.”



In the “The Perfect Theory” by Pedro Gil Ferreira



“Loop quantum gravity was the plucky competitor to string theory in its attempts to quantize gravity. Loop quantum gravity and its progeny offered a canonical alternative to string theory’s covariant approach. The devotees of loop quantum gravity made no attempt at unifying all the forces, but in taking geometry as their starting point, they tried to preserve some of the beauty of Einstein’s original idea in general relativity. Ironically, in the process, they abandoned the idea of spacetime as something fundamental.”



In the “The Perfect Theory” by Pedro Gil Ferreira





What always baffled when I started learning GR back in the day was whether it allowed causality violation. Ah, those were the days… now, probably more mature and also probably none the wiser, what can I add?

Do things have causes or do they just happen in ways we cannot predict? And the jury is not out on this at all: they happen in ways we just can't predict. This is not the right place to go into details on this, but, obviously, this is about Quantum Mechanics. And it's extremely tempting to say that, well, we can't predict these things because we don't yet understand some underlying mechanism ('hidden variables'). Some moderately famous physicists have thought this (that person who won a Nobel Prize for the photoelectric effect for one). And that turns out not to work in a particularly horrible way. John Bell proved a nice theorem which showed two things: first of all how to check whether the predictions of QM are valid, and secondly that if the predictions of QM are valid, then if such an underlying mechanism existed, we could use it to construct a time machine (technically 'hidden variables are nonlocal').

And we have checked, very carefully and very many times, and the world works the way QM says it does: 'the Bell inequalities are violated' in the jargon.

And so we're in a serious bind: either there is an underlying mechanism which we can then straightforwardly use to send information into the past and thus violate causality in the most horrible way, or things just happen in ways which can't be predicted even in principle. There is no third option. And, well, that's really awkward: no-one wants the world to be like that I think. But since we're scientists and not pontificators, we go and look at the world and believe what it tells us, even when it tells us things that we find awkward and conceptually difficult.

We know that GR predicts something called a singularity. I think I can confidently say that people assume that singularities are unphysical: they're a sign that GR is wrong in this limit.

To resolve that problem we need a better theory, which will presumably be a quantum theory of gravity. We don't have such a theory and (hype notwithstanding) we are not very close to having one, not least because it's absurdly hard to think up experiments which would give us any kind of test of such a theory or generally let the world tell us what kind of theory we need. Because such experiments are all-but-impossible we've been in a situation for a long time where a bunch of theoretical physicists have let their imaginations free-run and come up with all sorts of untestable ideas. We pretty clearly (I think) need to accept that either we will never know, or that some clever experimentalist will come up with some experiments which can be done and these will guide us. The latter is probably what will happen.

However, conveniently, none of this matters (if it did matter that would be an experiment!): black holes look like black holes whatever happens inside them, and we can never know what does happen inside them: the information is 'censored' from us by the event horizon. So we can rely on GR to tell us what BHs are like from the outside.

Intuitive ideas about space and time assume "flat" spacetime with an infinite maximum speed of causality. This means that it can be thought of more-or-less as a series of instants, each one a complete universe with no part of the frozen universe causing any other part, and each instant collectively causing the next instant. (Normally, we think of this as a continuum rather than a series of discrete instants, of course.)

This intuitive picture implies a lot of mathematical relationships that were formalized in detail by many people over the centuries, such as Euclid and Descartes. What Special and General Relativity say is simply that the relationships in the universe that lead to our understanding of space and time actually obey rules that are slightly different than what we naturally assume. Our normal conceptions of space and time are just a simpler approximation that is indistinguishable from reality to our senses in any situation we are normally in, which is why it is the way our brains evolved to conceive of reality. The mathematics of general relativity is more complicated, but equally self-consistent and could have been how we normally conceived of reality if we naturally experienced extreme relative velocities, accelerations and gravities. The idea that spacetime "bends" is essentially just a mathematical analogy. The mathematics of General Relativity, which has repeatedly been proven to be consistent with macroscopic observations, models the relative "locations" of events in space and time as points on a mathematical object called a Pseudo-Riemannian Manifold, which can be described using Gaussian coordinate systems.

This kind of mathematics was originally designed to describe geometry on curved surfaces, so the analogies to physical curvature are very close, although we can only make curved 2D surfaces in our (approximately) "flat" 3D space, not curved 4D ones, and the time coordinate does not actually enter the equations in the same way as a normal spatial coordinate. (This is dealt with using kind of a math trick that Minkowski came up with, whereby something like negative "distances" are used, and whether a "distance", or "spacetime-interval" between two events is positive or negative determines whether information/causation can pass between them. This weird "negative distance" is what makes the manifold PSEUDO-Riemannian, since this is not allowed in a true Riemannian manifold. Quantum physics does confuse all this, though.)

Whether or not this means that spacetime is "actually" curved does not change the effectiveness if the theory, and could easily be a pretty meaningless question. What modern physical experiments and the theories, such as General Relativity and Quantum Mechanics, required to explain them have shown us is that we must remember that things are not always as they appear at first, and that we carry a lot of unexamined assumptions that aren't really justified, as has sometimes been noted by philosophers even long before the twentieth century (It should also be noted that "curved" surfaces, in the mathematical sense of requiring these alternate mathematical systems to describe geometry, do not entirely correspond to the basic physical notion of "bending" even with "physical" 2D surfaces. For example, the surface wrapping around a cylinder (not counting the ends) is a mathematically "flat", i.e., Euclidean, plane, which corresponds to the fact that it can be unrolled to produce a physically flat surface).

After Pais’ “Subtle is the Lord” and Fölsing’s “Albert Einstein”, Gil Ferreira’s “The Perfect Theory” is a worthy complement to both.… (mehr)