The full question:
I like the question because it supposes that there is some kind of contradiction in the laws of physics. But the answer explains why there is not.If the Big Bang took only milliseconds to disperse all the galaxies light years apart, then how did the matter get there faster than the speed of light?
Top answer:
And it makes perfect sense.Let me clarify what Einstein’s theory says: It says that information cannot travel locally faster than light. For example, if there are two people, Alice and Bob, Einstein’s theory tells us that there’s no way that Alice can ever get a message to Bob along a particular pathway than it would take for light to travel along the same pathway. The reason I use emphasis there is because this is what Einstein means when he says that no information can travel locally faster than light. The “local” part is frequently overlooked because it’s subtle, and this leads to confusion.
If you shine a laser pointer at the moon for example and wiggle it around, then the target (on the moon’s surface) of your beam can move with arbitrary velocity (including speeds greater than light!). The point is though, you can convince yourself that you could never use this to communicate a message from one point on the moon’s surface, to another point faster than light.
So that’s what Einstein said, but what about in the balloon example? Well suppose Alice and Bob are located at the two dots on the balloon. As the balloon inflates, this is the analogue of the universe expanding, but no information is being transferred from Alice to Bob; no message/information is travelling at all in this instance. From this example it should be clear that even though the universe expands, and that objects may appear to recede (at super-luminal velocities in fact!), Einstein’s postulate isn’t violated at all, so there’s evidently no contradiction.
If Alice wanted to send a message to Bob in this example, even when the balloon is inflating, the message would still be constrained to travelling at less than the speed of light as it travels along its path, meaning that it could never reach Bob before a light-ray travelling along the same path and so all is good as far as Einstein is concerned.
You might wonder further, if the balloon inflated rapidly enough, would this mean (at some critical rate of expansion) that a message sent by Alice might never reach Bob, because a light ray send from Alice could never reach Bob due to the rate of expansion? * An analogue of this in nature is in fact true! Indeed, at a certain distance away from us called the cosmological horizon, the universe is expanding so rapidly that light from distances beyond this cannot reach us, and this is why the observable universe is of finite (growing) size. For this reason, everything we can see resides within the cosmological horizon. This is not at all to say that what we see is all there is, but that there’s a hard limit to the amount that we can see.
The bottom line is this: the fact that Einstein’s postulate is local means that it doesn’t depend on any particular pathway, it holds true for all of them. You can alter the path between the points A and B and you can still never transmit information along that path faster than you could send a light beam. We often pontificate that space is not matter etc. but the important point for this question is that the expansion of spacetime simply alters the lengths of (and angles between) pathways between any pair of points, and so the fact that Einstein’s postulate doesn’t depend on any particular pathway means that it naturally isn’t violated by the expansion of spacetime.
*As should be relatively clear if you picture it, the important factors at play here are not just how rapidly the balloon is inflating, but also how far the two dots on the balloon are from each other. For example, the distance between two points on the baloon, that are initially closer together, grows less rapidly than the distance between two dots with initially greater seperation.