I'm not quite sure how to ask this so that it can be answered in layman's terms, but I have lately seen, in several places, that with cosmological inflation, there was a point where the universe expanded faster than the speed of light.
In this explanation, the following is stated:
- Gravity itself would have split off at the Planck time, 1e-43 of a second
- The strong nuclear force by about 1e-35 of a second
- Within about 1e-32 of a second, the scalar fields would have done their work, doubling the size of the Universe at least once every 1e-34 of a second (some versions of inflation suggest even more rapid expansion than this).
It goes on to say that this rapid expansion is enough to take a quantum fluctuation 1e-20 times smaller than a proton and inflate it to a sphere about 10 cm across in about 15 x 1e-33 seconds.
The conclusion is that this expansion occurred at faster than light speed.
My main question is about the role of time in all of this, and I'm only indirectly interested in this apparent violation of the cosmic speed limit.
I have watched at least one interview (and I can't find a link to it right now) where a well-known physicist sums up the meaning of time as a big unknown, not being intuitively "fundamental" the way space is. However, in the very least, and perhaps most abstract way, time is an important part to the mathematics when it comes to explaining how things work.
My own understanding of time is that it is a way of gauging change relative to some known standard that is changing. (And acknowledging that it can change, depending on one's frame of reference.) That standard might be the swinging of a pendulum or the oscillations of some subatomic particle.
But in the earliest part of the universe's lifetime, before and during inflation, what was the standard for measuring time? Why would it be acceptable to say that the time duration of the inflationary period was so short and thus violated an accepted principle. Couldn't an alternative view be that the inflationary period lasted longer and nothing travelled faster than the speed of light? How was it decided that the duration of time for the inflationary period was so short?
Best Answer
This is a common point of confusion, not only with regards to inflation, but any time an expanding universe comes up...
The "cosmic speed limit" as you call it says that no particle or signal can move through spacetime faster than the speed of light. Spacetime is a very specifically defined thing, described with a coordinate system. There is no restriction, in terms of speed, on what spacetime itself is allowed to do. Let me illustrate with an example.
Imagine a photon. Relativity tells us that it always travels at speed $c$ (exactly at the speed limit). Let's say the photon has a path 10 light years long to travel along (remember light years are a measure of distance, $1\mathrm{ly} =$ the distance travelled by a photon in 1 year). The photon leaves and travels for 5 years, covering a distance of 5 light years. Then very suddenly, the universe doubles in size! The photon continues on its journey. The 5 remaining light years to travel have doubled in size, so it travels 10 more years to cover the last 10 light years. The journey has lasted 15 years. But the photon is now 20 light years from its starting point. Naively, we might compute its speed as $v = 20\mathrm{ly}/15\mathrm{yr} = \frac{4}{3}c$, faster than the speed of light. But in reality, it was just moving at speed $c$ the whole time in a universe that expanded.
In a more realistic scenario, the universe doesn't "suddenly" double in size, it does it gradually, but conceptually the same thing happens... you just need to use integrals to work out the math.
As to the meaning of time, that's somewhat more philosophical. However, I'll point out that, at least in general relativity, time is on an equal footing with space. Spacetime is described by a mathematical object called a metric. One example of a metric looks like:
$$ds^2 = c^2dt^2-dx^2-dy^2-dz^2$$
$x,y,z$ are the spatial coordinates and $t$ is the time coordinate; $s$ is a sort of generalized measure of spacetime length. As you can see, other than the constant $c$ (which could be set to equal 1 with a clever choice of units, so it's really rather unimportant), and a negative sign, time and space are equivalent in this formalism. If you understand space, then time should also make sense, as it's simply related to space by your "cosmic speed limit".