# Special relativity under the inflation of spacetime

• junglebeast

#### junglebeast

Inflation says that space between objects is expanding. Matter is held together by forces carried by bosons traveling at the speed of light. At the fringes of the universe inflation is warping space faster than the speed of light so it seems that there should be a horizon beyond which matter cannot exist (because even the strong force could not hold quarks together), but this also seems to violate the rule of special relativity that the speed of light should be the same in all inertial reference frames. Thoughts?

1) You need GR, not SR, to really treat expanding space-time well

2) There isn't any absolute velocity, so the expanding space-time at the "edge of the universe" is just the same as the expanding space-time where we are, at least according to relativity. Probalby you have some remanant of a belief in "absolute velocity" which makes you think that the space-time moving at a high velocity relative to you is different somehow because of its velocity. One of the priciples of relativity is that it doesn[t matter.

2) There isn't any absolute velocity, so the expanding space-time at the "edge of the universe" is just the same as the expanding space-time where we are, at least according to relativity. Probalby you have some remanant of a belief in "absolute velocity" which makes you think that the space-time moving at a high velocity relative to you is different somehow because of its velocity. One of the priciples of relativity is that it doesn[t matter.

Forget faster than light inflation for just a moment...why is it that the space between celestial bodies is increasing, but celestial bodies aren't coming apart? It must be that the internal attractive forces of celestial bodies are working to counteract the local expansion of space, which for the present is relatively insignificant here on Earth.

However if inflation is increasing exponentially, then at some future point in time, the inflation of spacetime where planet Earth is will occur faster than the speed of light...and then it will be impossible for Earth to continue to exist, because no matter what reference frame you look in, space is expanding faster than light, and bosons can't catch up. If inflation occurs uniformly everywhere in the universe, then this critical point will occur at all points in the universe simultaneously making it impossible for matter to exist anywhere in the universe. Yes?

Think about an expanding balloon with ants; of course the 'speed of expansion' and the speed of the ants are unrelated. c restricts the speed of ants, not the expansion.

Think about an expanding balloon with ants; of course the 'speed of expansion' and the speed of the ants are unrelated. c restricts the speed of ants, not the expansion.

Right...exactly...which leads to the questions I raised above

Right...exactly...which leads to the questions I raised above
You mean that "this also seems to violate the rule of special relativity that the speed of light should be the same in all inertial reference frames."
No!

Locally i.e. closed to the ant the ant-speed is always c. For ants which are far away or for the expansion of spacetime itself you simply can't define a unique speed in GR. Strictly speaking in GR 'speed' is only defined locally at one spacetime point. Taking a quasar and talking about its speed relative to the Earth is nonsense or at least not unique. There are definitions of speed which seem to violate the speed limit, but this is an artefact due to the definition.

However if inflation is increasing exponentially, then at some future point in time, the inflation of spacetime where planet Earth is will occur faster than the speed of light

No, it won't. In a curved spacetime, the statement "things can't move faster than light" has to be generalized, since as other posters have mentioned, there's no way to uniquely define a relative speed of two objects that are spatially separated. When generalized to curved spacetime, the statement becomes: "things can't move outside the local light cones". This means exactly the same thing as "things can't move faster than light" in SR, where spacetime is flat; but it generalizes easily to curved spacetimes, since at each event there are still light cones, defined by the metric.

In the inflation scenario, Earth (and every other object) always moves within the light cones at the local event where it is. The "expansion" of space means that, if you look at the light cones spread over a spacelike slice, they "tilt" as you go from one "side" of the universe to the other. But the tilting is a global effect; it's not observable locally. Locally, spacetime looks "normal" wherever you are, even if the tilting of the light cones somewhere across the universe from you is so extreme that that part apparently moves "faster than light" away from you.