# Faster than light in quantum gravity?

Imagine there's two objects a light second apart in a space with a certain metric. So no signal can reach the other under a second.

But in quantum gravity where we sum over metrics, there may be a metric that distorts space such that the two objects are closer together.

Does this mean that signals csn travel faster than light when taking into account quantum gravity effects?

This doesn't seem right. What is wrong with this argument?

In saying that the objects are one light-second apart, you have ruled out there being a metric that puts them at any other distance (distance is more or less defined by the metric). If you want to generalize metrics so that there can be more than one at once, you also have to let there be more than one distance at once. In setting up the problem you ruled out the metrics that are being considered.

• They are 1 second apart with in a space with a given metric. But under quantum gravity you sum over all possible spacetime curvatures right? There arent more than one metric but a superposition of all possible metrics
– user84158
Commented Oct 11, 2018 at 19:42
• In regular quantum mechanics it is easy to construct superpositions of multiple particle distances: superluminal messaging is then ruled out by the behavior of measurement. There may be some aspect of quantum gravity that I'm not aware of that makes it a problem, of course, but at first glance there seems to be nothing wrong. It only appears to be a paradox when you apply causality in a space with a particular metric, which doesn't have much to do with the superposition of metrics where it appears to be violated. Commented Oct 11, 2018 at 21:11
• Good point. The measurement of a message will "collapse" the metric into a certain state which will then show that the message travelled subluminally over that manifold. Makes sense.
– user84158
Commented Oct 11, 2018 at 21:58

In some quantum gravity models (actually most of them) you can meet the dimensional reduction phenomena. Spacetime effectively behaves as it was 2 (or lower) dimensional. The reason is the fractality of spacetime at the lowest scales. Then modelled particles can become superluminar. See example: in Causal Dynamical Triangulations .

It was observed in numerical simulations that the speed of light got altered / lorentz invariance got violated by anomalous scaling of time.