**Einstein's one tiny problem**

Otherwise solid, the theory of general relativity starts to melt at the quantum level

Nov 06, 2005 08:30 AM

Fotini Markopoulou Kalamara

Special to the Star

What did Einstein do better than Newton? He said that space-time is not a neutral stage on which other stuff matter moves, but it is itself made of all the processes that take place in the world and all their coincidences, or events.

Thus space-time becomes dynamic, alive in a sense; it is a collective of everything that affects every single constituent inside it. That led Einstein to general relativity, in which space-time is a geometry that tells matter where to go, and matter tells space-time how to curve.

That is all very beautiful. But now consider the other great discovery of last century, quantum physics. At the level of elementary particles, matter is subject to the laws of quantum theory. Quantum theory says that ultimately the notion of a path and thus an event the coincidence of two paths is not as straightforward as the geometric beauty of general relativity would have us believe. If I send an elementary particle from home to work, general relativity says it will take the shortest path. Quantum theory says that it will take all possible paths at the same time, with consequences we've tested to great experimental accuracy.

This is really a bad blow to the pretty picture of space-time geometry. If a particle ceases to have a well-defined position, then how does it tell space-time how to curve? Does every single path the particle takes curve space-time in a different way? What happens to general relativity's basic principle, that matter tells space-time how to curve and space-time tells matter where to go? Does one elementary particle on a given space-time create a subsequent superposition of space-times?

At the very least, these questions mean that general relativity is not the final theory of space-time. The quantumness of matter has to be incorporated into the theory in a consistent and coherent manner, or we have a problem.

How big is this problem? We might try to console ourselves that, for the quantum effects to be significant, one has to have very small mass, and with a small mass you can only curve space-time so little that the effect of the one particle is extremely small. You might see it near a black hole, or near the beginning of the universe.

But this argument has, in fact, left out general relativity. It only applies to one, fixed space-time with one particle in it.

Let's remember that the basic principle that Einstein used as a guide to special and general relativity is that it is physical processes and their coincidences events that are fundamental, and space-time is the collection of all of those.

But he considered classical processes and classical events. Our task includes repeating the exercise for quantum processes and events, since at the basic level the world is made of quantum systems squillions of quantum particles that have to make up a space-time.

The question cannot be what happens to a given space-time when it contains a quantum particle but the other way around: How did the true constituents of the universe combine to create a space-time, a construction that makes us think that the notion of a path is natural and, with matter, an entity separate from space-time?

Ultimately, we still don't know precisely what question we should be asking. General relativity is considered a fundamental theory not least because we believe that the notion of space-time is fundamental: It is everywhere.

I believe the real lesson of quantum theory is that the space-time description of the world is good, but not fundamental. It tells us that the notion of a particle's path does not exist, and the way we deal with that is to talk of a particle taking all possible paths at the same time.

How do we go about discovering the real question to ask? We ask preliminary questions, a bunch of different ones. For example, let us say it's true that there is such a thing as a quantum superposition of space-times. What does it look like?

If you like that question, you might want to do research on Loop Quantum Gravity, an approach whose goal is a quantum version of general relativity, keeping very close to all the principles of relativity and the notion that space-time is fundamental.

The aim is to find a consistent and sensible description of such a space-time. If it exists and can be checked to be correct, then you will have learned something profound about space-time.

The first indications from this approach suggest a relational picture of space, where the geometry is replaced by a network of connectivities. It also suggests a fundamental finiteness: General relativity says that if you look inside a small region of space, you could magnify it arbitrarily and there would be more and more new things to look at, while the network picture indicates there is a limit. At some point your magnifying glass does not see any new network connections. There can only be a finite amount of information in a finite region of space.

But that is still not enough. You have to understand what quantum space-time means; in fact, what space-time means if it is quantum. It is one thing to have an elementary particle take all possible paths simultaneously, but space-time refers to what is past and what is future. What can I mean by future if something is and is not in it at the same time?

Conversely, you might think that it is peculiar to think of space-time and matter as separate things. The very interconnectivity of the two could mean that it is wrong to address questions purely on the relativity front, as Loop Quantum Gravity mostly does, and you should instead look for a unified theory.

You may want to work on String Theory. This unification suggests a picture of the world that contains extended objects strings and membranes instead of the ordinary point objects that electrons and protons basically are. Your relationship with space-time will be complicated. Your extended objects live in some sort of fixed space-time, usually of a higher dimension than we do, but which is not necessarily our space-time. In fact, it had better not be our space-time, because it is fixed and not dynamic.

Or you might find such approaches unsatisfactory; too baroque and intricate, not enough physics. You'd rather be the "practical" type. You might start by stating what we know: The world started as an extremely hot, high-energy soup. Planck temperature hot, compared to which the centre of the hottest star is freezing cold.

Maybe the notion of a space-time does not make any sense at all, quantum or not, at this early stage. It is plausible that space-time only emerged as the universe cooled down, and is thus not fundamental. Space-time is the frozen phase of whatever makes up the universe, just as ice is a phase of a collection of water molecules that emerges from water when we cool it down. Ice has a regularity, a solid structure that water does not have. Maybe such a regularity is all we can mean by space-time.

The optimist in this approach will say that the fact that space-time is everywhere must mean that it is natural. Its very universality must mean its reason for existence is simple and so we should be able to find that reason.

This is very attractive in its simplicity. Nonetheless, it is hard enough to show how ice emerges from water even though we have bucket loads of it to study and we know that it does, let alone understand how space-time emerges from something we do not yet perceive. It's a bit like living in a world of ice that never melts: Would you know that water is a possibility?

Einstein broke the mould and showed that space-time is not given, fixed and frozen. We still have not taken this to its natural conclusion and found out what space-time really is. To get there, we need such a fundamental rethinking of our notion of space-time that it's hard to even guess what the consequences will be. It's hard to think outside the box when the box is space-time.

http://www.thestar.com/ScienceTech/article/138817