Does the expansion of the Universe break the speed of light? - Beyond The World
Universe

Does the expansion of the Universe break the speed of light?

The cardinal rule of relativity is that there’s a speed limit to the Universe, the speed of light, that nothing can break. When we look at the most distant objects, their light has only been traveling for 13.8 billion years, yet it looks much farther away. That, however, does not break the speed of light; it only destroys our outdated, intuitive conceptions of how reality should behave.

If most people know one rule about the Universe, it’s that there is an ultimate speed limit that nothing can surpass: the speed of light in a vacuum. If you’re a big particle, you can’t just not exceed that speed, but you’ll never achieve it; you can only approach it. If you have no mass, you can only move through spacetime at one speed: the speed of light if you’re in a vacuum, or a slower speed if you’re in a medium. The quicker you move in space, the slower you move in time, and vice versa. These truths cannot be avoided since they are the fundamental principle upon which relativity is based.

Yet, when we look out into the Universe, distant things appear to defy our common-sense logic. We know the Universe is 13.8 billion years old because of a series of accurate measurements. The most distant galaxy we’ve seen thus far is 32 billion light-years away; the most distant light we see corresponds to a location 46.1 billion light-years away; and galaxies beyond around 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 violates the laws of relativity or the speed of light; it simply violates our intuitive assumptions of how things should behave. Here are some facts about the expanding Universe and the speed of light that everyone should be aware of.

Putting a mass down causes what would have been ‘straight’ lines to become curved by a specified amount instead of an empty, blank, three-dimensional grid. We treat space and time as continuous in General Relativity, but all types of energy, including but not limited to mass, contribute to spacetime curvature. Furthermore, as the cosmos expands, the distances between unbound things change over time. (Credit: Christopher Vitale of Networkologies and the Pratt Institute.)

What “nothing can travel faster than the speed of light” actually means

It is true: nothing can travel faster than the speed of light. But what does that actually mean? Most people, when they hear it, think the following thoughts:

  • When I observe an object, I can follow its movement and see how its location changes over time.
  • When I see it, I may note its observed position as well as the time I saw it.
  • Then I may estimate its velocity by applying the definition of velocity, which is a change in distance divided by a change in time.
  • 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 everyday experiences, but it is not universal. All of this, in particular, includes an assumption that we hardly never evaluate, let alone state.

What is the questionable assumption? That space is flat, uncurved, and unchanging. This happens in Euclidean space, which is the sort of space we normally imagine when we think of our three-dimensional Universe. Most of us envision doing something like putting down a three-dimensional “grid” on top of everything we see and trying to describe positions and times with a set of four coordinates, one for each of the x, y, z, and time dimensions.

Even in an expanding cosmos, light produced by a distant object will reach our eyes given enough time. However, if the recession speed of a distant galaxy exceeds and remains above the speed of light, we will never be able to reach it, even if we can receive light from its ancient past. (Credit: Larry McNish/RASC Calgary)

In other words, most of us understand the basic concept of special relativity — the “nothing can move faster than light” part — but fail to see that special relativity alone cannot adequately represent the real Universe. 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 obeys those laws of special relativity.

What isn’t captured in our common understanding is how the fabric of space detracts from this idealized, flat, and three-dimensional grid, where each successive moment is characterized by a universally applicable clock. Instead, we must acknowledge that our Universe follows Einstein’s General Relativity principles, and that those rules govern how spacetime evolves. In particular:

  • space itself can either expand or contract
  • space itself can be either positively or negatively curved, not only flat
  • the laws of relativity apply to objects as they move through space, not to space itself

In other words, when we say “nothing can move faster than light,” we mean “nothing can move faster than light through space,” yet the motion of objects through space tells us nothing about the evolution of space itself. Alternatively, nothing moves faster than light relative to another item at the same point, or event, in spacetime.

Edwin Hubble’s original map of galaxy distances vs redshift (left), which established the expanding cosmos, compared to a more recent counterpart from around 70 years later (right). The cosmos is expanding, as both observation and theory suggest. (Credit: E. Hubble; R. Kirshner, PNAS, 2004)

Space doesn’t expand at a speed

So, nothing moves faster than light across space, but what about how space changes? You’ve probably heard that we live in an expanding Universe, and that the rate at which the fabric of space itself grows has been measured: the Hubble constant. We’ve even exactly measured that rate and can be certain, based on all of our measurements and observations, 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?

For every megaparsec (about 3.26 million light-years) away that a distant and unbound object is from us, we’ll see it recede from us as though it were moving away at the equivalent of 66-74 km/s. If something is 20 Mpc distant from us, we should expect it to move away at the equivalent of 1320-1480 km/s; if it’s 5000 Mpc away, we should expect it to move away at 330,000-370,000 km/s.

However, this is confusing for two reasons. One, it is not travelling at that speed through space; rather, this is the consequence of the distance between objects expanding. And two, the speed of light is 299,792 km/s, so isn’t that hypothetical object that’s ~5000 Mpc away actually moving away from us at speeds exceeding the speed of light?

The raisin bread model of the expanding Universe, in which relative distances grow as space (dough) expands. The larger the observed redshift by time the light is received, the greater the distance between any two raisins. The redshift-distance relation anticipated by the expanding Universe has been confirmed by observations and has been consistent with what’s been known all the way back since the 1920s. (Credit: NASA/WMAP Science Team.)

The “raisin bread” model is how I prefer to think about the growing Universe. Imagine you have a ball of dough with raisins all over it. Observe how the dough expands in all directions because it leavens. (You may also imagine this happening in a zero-gravity setting, such as the International Space Station.) What do you notice the other raisins doing if you put your finger down on one raisin?

  • 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.

In this analogy, the raisins represent galaxies or bound groups/clusters of galaxies, while the dough represents the expanding Universe. However, in this approach, the dough that represents the fabric of space cannot be seen or directly detected, does not get less dense as the Universe expands, and just serves as a “stage” for the raisins, or galaxies, to inhabit.

While matter and radiation grow less dense as the Universe expands due to its increasing volume, dark energy is a kind of energy that exists entirely of space. The density of dark energy remains constant as new space is created in the expanding Universe. (Credit: E. Siegel/Beyond the Galaxy)

Because the rate of expansion is determined by the total amount of “stuff” in a particular volume of space, as the Universe expands, it dilutes and the rate of expansion decreases. Because matter and radiation are made up of a constant number of particles, the density of matter and radiation both decrease as the Universe expands and the volume increases. Because radiation’s energy is determined by its wavelength, and as the Universe expands, that wavelength stretches as well, causing it to lose energy, the density of radiation reduces somewhat faster than the density of matter.

On the other hand, the “dough” itself contains a limited, positive, non-zero amount of energy in every area of space, and that energy density remains constant as the Universe expands. While the densities of matter and radiation decrease, the energy of the “dough” (or space) itself remains constant, and this is what we call dark energy. We may confidently conclude that the energy budget of our real Universe, which comprises all three of them, was dominated by radiation for the first few thousand years, then by matter for the next few billion years, and finally by dark energy thereafter. As far as we can tell, dark energy will permanently dominate the Universe.

The predicted destiny of the Universe (top three illustrations) all relate to a Universe in which matter and energy work against the original expansion rate. In our observed Universe, a cosmic acceleration is caused by some type of dark energy, which is hitherto unexplained. The Friedmann equations govern all of these Universes, which relate the expansion of the Universe to the various forms of matter and energy existing inside it. (Credit: E. Siegel/Beyond the Galaxy)

Now, here’s the tricky part. 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

Fortunately, the first part is usually extremely short. The second part is known as unusual velocity, and it can range from hundreds to hundreds of kilometers per second.

This simplified animation shows how light redshifts and unbound object distances vary over time in the expanding Universe. Note that the objects start off closer than the amount of time it takes light to travel between them, the light redshifts due to the expansion of space, and the two galaxies wind up much farther apart than the light-travel path taken by the photon exchanged between them. (Credit: Rob Knop.)

Nevertheless, the third element is the consequence of cosmic expansion. It is always the dominant effect at distances greater than around 100 megaparsecs. On the largest cosmic scales, the Universe’s expansion is all that matters. What’s important to understand is that the expansion has no intrinsic speed; space expands at a frequency: a speed per unit distance. Expressing it as kilometers-per-second-per-megaparsec obscures the fact that “kilometers” and “megaparsecs” are both distances, and transforming one into the other balances them out.

Light from distant objects is actually redshifted, but not because anything is receding faster than light or expanding faster than light. Space simply expands; it’s us who shoehorns in a “speed” because that’s what we’re familiar with.

Whatever the expansion rate is now, together with whatever kinds of matter and energy exist in your universe, will determine how redshift and distance are connected in our universe for extragalactic objects. (Credit: Ned Wright/Betoule et al. (2014))

What’s actually accelerating in our accelerating Universe?

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 may also measure its redshift, or how the light is “shifted” from what it would be if we were in the same location and under the exact conditions where it was emitted. That shift, because of our familiarity with how waves shift due to the Doppler effect (such as for sound waves), is something we often translate into a recession speed.

However, we are not measuring real speed; instead, we are measuring the sum of movements plus the effect of the expanding Universe. When we say “the Universe is accelerating,” what we mean 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, giving the impression that it is accelerating away from you.

In reality, the redshift is caused by the expansion of space, not by the galaxy speeding away from you. If we were to really measure the expansion rate over time, it would continue to decrease and finally asymptote to a finite, positive, and non-zero value; this is what it means to live in a dark energy-dominated Universe.

The visible Universe’s size (yellow), as well as the amount we can reach (magenta). The observable Universe has a limit of 46.1 billion light-years because that is how far away an object that emitted light that is only now reaching us would be after expanding away from us for 13.8 billion years. However, humans can never approach a galaxy beyond around 18 billion light-years, even if we travel at the speed of light. (Credit: Andrew Z. Colvin and Frederic Michel, Wikimedia Commons; Annotations: E. Siegel)

So what determines “distance” in an expanding Universe?

When we talk about the distance to an item in the expanding Universe, we’re always taking a cosmic picture — a kind of “God’s eye view” — of how things are right now: when the light from these distant objects arrives. We know we’re seeing these things as they were in the ancient past, not as they are now (13.8 billion years after the Big Bang), but as they were when they generated the light we see today.

When we ask, “How far away is this object?” we are not asking how far away it was from us when it emitted the light we are now seeing, nor how long the light has been in transit. Instead, we’re wondering how far away the object is from us right now, if we could somehow “freeze” the expansion of the Universe. The most distantly seen galaxy, GN-z11, emitted its now-arriving light 13.4 billion years ago and is 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.

However, just because you can see it does not mean you can reach it. Any object that is currently more than 18 billion light-years away from us will continue to emit light, and that light will move across the Universe, but the fabric of space will simply grow too fast for it to ever reach us. Every unbound object moves further and further away with each passing moment, and previously reachable things transition across that mark to become permanently unreachable. In an expanding Universe, nothing goes faster than light, that is 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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