# Is there any limit on movement of space itself?

According to special relativity, c is the maximum speed at which all matter and information in the universe can travel. [IN SPACE]

But the inflationary hypothesis says the space itself expanded faster than the speed of light. Is there any theoretical limit on how fast can the space itself move?

• Space doesn't move. The expansion of space is very different from ordinary movement. – ACuriousMind Nov 20 '14 at 12:54
• How is it different? Does the space not move when gravitation waves propagate through it? – daniel.sedlacek Nov 20 '14 at 15:23
• Movement is the phenomenon that the space coordinate of a thing varies with time. A point in space does not have a coordinate, since it is the coordinate. Space cannot move because there is nothing it could move through (like ordinary things move through space). – ACuriousMind Nov 20 '14 at 15:30
• So space can expand, warp, wave, bend, distort but not move. Got it. So is there a limit at which can space move but not move? – daniel.sedlacek Nov 20 '14 at 15:43
• I think the downvotes are unkind. It seems obvious what Daniel is asking, and quibbling over the use of the word move seems ungracious to me. Instead of downvoting, why not answer and as part of the answer explain why spacetime doesn't move? – John Rennie Nov 20 '14 at 15:52

It's tempting to think of spacetime as a thing, and it doesn't help that it's often represented as a rubber sheet in popular science programmes. In relativity (special and general) spacetime is a mathematical concept - it is a manifold equipped with a metric. At the risk of over-simplifying, a manifold is a thing that has dimensionality (four dimensions for spacetime) and a metric is a function that defines distances between points in the spacetime.

When we talk about spacetime expand this is a somewhat careless shorthand for what is actually going on. What we actually mean is that the metric is a function of time. because it's the metric that determines the distances between points in spacetime, this means that the distances between points in spacetime is also a function of time. In the particular case of the our universe the metric that (approximately) describes our spacetime is the FLRW metric, and the distance between any two spacetime points is proportional to a function called the scale factor. My answer to Did the Big Bang happen at a point? explains how we calculate the scale factor and includes this graph of its variation with time:

It's immediately obvious that the scale factor increases with time, and that's why we (somewhat carelessly) say the universe is expanding.

Assuming you've stuck it this far I can now answer your question, because there is in principle no limit to how fast the scale factor can increase with time. You've no doubt read startling statics like during inflation the universe expanded by a factor of $10^{26}$ in less than $10^{-32}$ seconds, but the expansion rate could have been arbitrarily large. It just depends on the value of the inflaton field. Of course, excessively large values of the inflation field may not produce a universe that looks like ours, so there are limits placed by observation. However there is no fundamental restriction imposed by general relativity to how fast the scale factor could have increased.

A few quick footnotes:

In a comment you ask whether space doesn't move when a gravitational wave passes through it. Again the temptation is to think of a gravitational wave as a ripple on water or a vibration in a rubber sheet. A gravitational wave is actually a time dependant change in the metric. If we are measuring distances, using the metric, then when a gravity wave passes by we will see the measured distances changing with time because the metric changes with time. If we're being lazy we'd say the spacetime is oscillating, but really what we mean is that the metric is oscillating.

• Every metaphor is imperfect simplification but that shouldn't prevent scientist from explaining concepts to layman. Strangely you don't like the rubber sheet metaphor - I used to think about objects in space as smarties in jello - if they are tunnelling through the jello they are moving. If the jello itself is warping bringing two objects closer or further then they were without them tunnelling through the jello then the space is moving while the objects are not moving. Or is this metaphor too far from reality? – daniel.sedlacek Nov 20 '14 at 18:01
• @daniel.sedlacek: the rubber sheet analogy, or your Jello metaphor, are useful for giving a rough idea of how GR works. But they mislead in some important ways. For example they only show curvature of space, but in most cases you and I are likely to encounter curvature of the time coordinate dominates. Anyone seeking to understand how GR really works would be wise to discard the rubber sheet/jello analogy. – John Rennie Nov 21 '14 at 7:05