Was Einstein wrong when he said nothing can go faster than the speed of light?

Question

If the universe is constantly expanding faster than the speed of light, how could Einstein be right?

Answer 1

In SR, there are global inertial reference frames and, in this context,

no object moving with speed less than c in one reference frame moves with speed equal to or greater than c in any reference frame.

But, in GR, in a curved spacetime,

there are no global inertial reference frames.

Instead, there are local inertial reference frames. We say that, tangent to each event in spacetime is a flat spacetime, i.e., in the infinitesimal neighborhood of an event, spacetime is flat to first order.

So, in this tangent spacetime, SR holds.

But, we must be much more careful in a general spacetime as in, for example, a universe undergoing a metric expansion of space.

In such a spacetime, the very notion of distance and relative speed is far more subtle and complex than in the flat spacetime of SR. In fact, there are multiple notions of distance and relative speed that must be 'grokked' to sort all of this out.

From the Wikipedia article linked above:

Because this expansion is caused by relative changes in the distance-defining metric, this expansion (and the resultant movement apart of objects) is not restricted by the speed of light upper bound of special relativity which is a constraint only on the speed matter can obtain from boosts from one reference frame to another. Two references frames that are globally separated can be moving apart faster than light without violating special relativity, though whenever two reference frames diverge from each other faster than the speed of light, there will be observable effects associated with such situations including the existence of various cosmological horizons.

In other words, one must be very careful in translating results from the flat spacetime of SR to the curved spacetime of GR.

Answer 2

A better way to think of it would be that space is being added to the universe; the universe is not "moving".

Consider the case of two stars. The expansion of the universe doesn't cause the stars to "move" away from each other. Rather, space is created between the stars, resulting in them being further apart.

This consequently, doesn't violate general relativity.

Answer 3

In Special Theory of Relativity, all inertial reference frames are able to communicate with each other to share their results. And, they all agree with the value of c and related conclusions.

In General Theory of Relativity, it's not always true. There are situations when two inertial reference frames may not be able to communicate with each other. In such situations, Einstein's Relativity is no longer valid as we have no way to compare results of both reference frames.

When it comes to universe's expansion (which is actually expansion of Spacetime) and we calculate speed of a point on one edge of universe with respect to a point on opposite edge of the universe, we actually cheat. We aren't allowed for such calculations as per General Theory of Relativity. Both points are separated in such a way that reference frames attached to them can't communicate with each other. That's it.