If there’s one rule that most people know about the Universe, it’s that there’s an ultimate speed limit that nothing can exceed: the speed of light in a vacuum. If you’re a massive particle, not only can’t you exceed that speed, but you’ll never reach it; you can only approach the speed of light. If you’re massless, you have no choice; you can only move at one speed through spacetime: the speed of light if you’re in a vacuum, or some slower speed if you’re in a medium. The faster your motion through space, the slower your motion through time, and vice versa. There’s no way around these facts, as they’re the fundamental principle on which relativity is based.
And yet, when we look out at distant objects in the Universe, they seem to defy our common-sense approach to logic. Through a series of precise observations, we’re confident that the Universe is precisely 13.8 billion years old. The most distant galaxy we’ve seen so far is presently 32 billion light-years away; the most distant light we see corresponds to a point presently 46.1 billion light-years away; and galaxies beyond about 18 billion light-years away can never be reached by us, even if we sent a signal at the speed of light today.
Still, none of this breaks the speed of light or the
laws of relativity; it only breaks our intuitive notions of how things ought to
behave. Here’s what everyone should know about the expanding Universe and the
speed of light.
Understanding the Basics of Special Relativity:
When I observe an object, I can track its motion, observing how its position changes over time. When I see it, I can record its observed position and the time at which I observe it. Then, by using the definition of velocity — that it’s a change in distance divided by a change in time — I can get its velocity. Therefore, whether looking at a massive or massless object, I had better observe that the velocity I get never exceeds the speed of light, or that would violate the laws of relativity. This is true in most of our common experience, but it isn’t true universally. In particular, all of this includes an assumption that we pretty much never think about, much less state.
The assumption in question? That space is flat,
uncurved, and unchanging. This occurs in Euclidean space: the type of space we
normally conceive of when we think about our three-dimensional Universe.
Einstein’s General Relativity:
In other words, most of us understand the basic concept of special relativity — the “nothing can move faster than light” part — but fail to appreciate that the real Universe cannot accurately be described by special relativity alone. Instead, we need to take into account that the Universe has a dynamical fabric of spacetime underpinning it, and that it’s only the motion of objects through that spacetime which obey those laws of special relativity.
What isn’t encapsulated in our common conception is the ways that the fabric of space departs from this idealized, flat, and three-dimensional grid, where each successive moment is described by a universally applicable clock. Instead, we have to recognize that our Universe obeys the rules of Einstein’s General Relativity, and that those rules dictate how spacetime evolves.
Expanding Universe and the Hubble Constant:
So, nothing can move faster than light through
space, but what about the ways that space itself changes? You’ve likely heard
that we live in an expanding Universe, and that we’ve measured the rate at
which the fabric of space itself expands: the Hubble constant. We’ve even
measured that rate precisely well, and can be certain, from all the
measurements and observations we’ve taken, that the present-day rate of
expansion is precisely between 66 and 74 km/s/Mpc:
kilometers-per-second-per-megaparsec.
But what does it mean that space is expanding?
Raisin Bread Analogy:
The way I like to think about the expanding Universe is with the “raisin bread” model. Imagine that you have a ball of dough with raisins all throughout it. Now imagine that the dough leavens, expanding in all directions. (If you like, you can further imagine this is happening in a zero-gravity environment, like on the International Space Station.) Now, if you put your finger down on one raisin, what do you see the other raisins doing?
The closest raisins to you will appear to move slowly away from you, as the dough between them expands. Raisins that are farther away will appear to be moving away more quickly, as there’s more dough between them and you than the closer raisins. Raisins that are even farther away will appear to be moving away ever more-and-more quickly.
Energy Density and Dark Energy:
The rate of expansion is dependent on the total amount of “stuff” in a given volume of space, so as the Universe expands, it dilutes and the expansion rate drops. Because matter and radiation are made up of a fixed number of particles, as the Universe expands and the volume increases, the density of matter and radiation both drop. The density of radiation drops a little faster than the density of matter, because radiation’s energy is defined by its wavelength, and as the Universe expands, that wavelength stretches as well, causing it to lose energy.
On the other hand, the “dough” itself contains a finite, positive, non-zero amount of energy in every region of space, and as the Universe expands, that energy density remains constant. While the matter and radiation densities drop, the energy of the “dough” (or space) itself remains constant, and that’s what we observe as dark energy.
Redshift and the Expanding Universe:
Every time we look at a distant galaxy, we’re seeing the light from it as it is right now: upon its arrival. That means the light that was emitted experiences a slew of combined effects: the difference between the gravitational potential from where it was emitted to where it arrives, the difference in the motion of the emitting object through its space and the motion of the absorbing object through its local space, the cumulative effects of the expansion of the Universe, which stretch the light’s wavelength.
The first part, thankfully, is normally very small. The second part is known as peculiar velocity, which can range from hundreds up to a few thousand kilometers-per-second. But the third part is the effect of cosmic expansion. At distances of more than about ~100 megaparsecs or so, it’s always the dominant effect.
Challenges of Measurement:
One difficulty that we have is that we can’t actually measure the speed of a distant object. We can measure its distance through a variety of proxies, like how bright/faint it is or how large/small it appears on the sky, presuming we know or can figure out how intrinsically bright or large it is. We can also measure its redshift, or how the light is “shifted” from how it would be if we were in the precise location and under the same precise conditions where the light was emitted.
However, we’re not measuring an actual speed; we’re measuring the cumulative effects of motions plus the effect of the expanding Universe. When we say “the Universe is accelerating,” what we actually mean — and this is not what you’d intuit at all — is that if you watch the same object as the Universe expands, it will not only continue to increase in distance from you, getting farther and farther away, but the light that you receive from this object will continue to display an ever-increasing redshift, which makes it seem as though it’s accelerating away from you.
In reality, though, the redshift is due to the expansion of space, not to the galaxy speeding away from you faster and faster. The expansion rate, if we were to actually measure that over time, is still decreasing, and will eventually asymptote to a finite, positive, and non-zero value; that’s what it means to live in a dark energy-dominated Universe.
Understanding Cosmic Distance:
When we talk about the distance to an object in the
expanding Universe, we’re always taking a cosmic snapshot — a sort of “God’s
eye view” — of how things are at this particular instant in time: when the
light from these distant objects arrives. We know that we’re seeing these
objects as they were in the distant past, not as they are today — some 13.8
billion years after the Big Bang — but rather as they were when they emitted
the light that arrives today.
But when we talk about, “how far away is this object,” we’re not asking how far away it was from us when it emitted the light we’re now seeing, and we aren’t asking how long the light has been in transit. Instead, we’re asking how far away the object, if we could somehow “freeze” the expansion of the Universe right now, is located from us at this very instant.
The farthest observed galaxy GN-z11, emitted its now-arriving light 13.4 billion years ago, and is located some 32 billion light-years away. If we could see all the way back to the instant of the Big Bang, we’d be seeing 46.1 billion light-years away, and if we wanted to know the most distant object whose light hasn’t yet reached us, but will someday, that’s presently a distance of ~61 billion light-years away: the future visibility limit.
Just because you can see it, though, doesn’t mean
you can reach it. Any object presently beyond 18 billion light-years from us
will still emit light, and that light will travel through the Universe, but the
fabric of space will simply expand too relentlessly for it to ever reach us.
With each moment that passes, every unbound object moves farther and farther
away, and previously reachable objects transition across that mark to become
forever unreachable. Nothing moves faster than light in an expanding Universe,
and that’s both a blessing and a curse. Unless we figure out how to overcome
this, all but the closest galaxies may forever be beyond our reach.
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