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Starts With A Bang

Ask Ethan: How Can We See 46.1 Billion Light-Years Away In A 13.8 Billion Year Old Universe?

In General Relativity, the fabric of space doesn’t remain static over time. Everything else depends on the details we measure.

If there’s one thing we’ve experimentally determined to be a constant in the Universe, it’s the speed of light in a vacuum, c. No matter where, when, or in which direction light travels, it moves at 299,792,458 meters-per-second, traveling a distance of 1 light-year (about 9 trillion km) every year. It’s been 13.8 billion years since the Big Bang, which might lead you to expect that the farthest objects we can possibly see are 13.8 billion light-years away. But not only isn’t that true, the farthest distance we can see is more than three times as remote: 46.1 billion light-years. How can we see so far away? That’s what Anton Scheepers and Jere Singleton want to know, asking:

If the age of the universe is 13.8 billion years, how can we detect any signal that is more than 13.8 billion light-years away?

It’s a good question, and one that you need a little bit of physics to answer.

We often visualize space as a 3D grid, even though this is a frame-dependent oversimplification when we consider the concept of spacetime. In reality, spacetime is curved by the presence of matter-and-energy, and distances are not fixed but rather can evolve as the Universe expands or contracts. (REUNMEDIA / STORYBLOCKS)

We can start by imagining a Universe where the most distant objects we could see really were 13.8 billion light-years away. For that to be the case, you’d have to have a Universe where:

  • objects remained at the same, fixed distance from one another over time,
  • where the fabric of space remained static and neither expanded nor contracted over time,
  • and where light propagated through the Universe in a straight line between any two points, never being diverted or affected by the effects of matter, energy, spatial curvature, or anything else.

If you imagine your Universe to be a three-dimensional grid — with an x, y, and z axis — where space itself is fixed and unchanging, this would actually be possible. Objects would emit light in the distant past, that light would travel through the Universe until it arrived at our eyes, and we’d receive it the same number of “years” later as the number of “light-years” the light traveled.

In a static, unchanging Universe, all objects would emit light in all directions, and that light would propagate through the Universe at the speed of light. After a time of 13.8 billion years had passed, the maximum amount of distance that the light could have traveled would be 13.8 billion light-years. (ANDREW Z. COLVIN OF WIKIMEDIA COMMONS)

Unfortunately for us, all three of those assumptions are incorrect. For starters, objects don’t remain at a constant, fixed distance from one another, but rather are free to move through the space that they occupy. The mutual gravitational effects of all the massive and energy-containing objects in the Universe cause them to move around and accelerate, clumping masses together into structures like galaxies and clusters of galaxies, while other regions become devoid of matter.

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These forces can get extremely complex, kicking stars and gas out of galaxies, creating ultra-fast hypervelocity objects, and creating all sorts of accelerations. The light that we perceive will be redshifted or blueshifted dependent on our relative velocity to the object we’re observing, and the light-travel time won’t necessarily be the same as the actual present-day distance between any two objects.

A light-emitting object moving relative to an observer will have the light that it emits appear shifted dependent on the location of an observer. Someone on the left will see the source moving away from it, and hence the light will be redshifted; someone to the right of the source will see it blueshifted, or shifted to higher frequencies, as the source moves towards it. (WIKIMEDIA COMMONS USER TXALIEN)

This last point is very important, because even in a Universe where space is static, fixed, and unchanging, objects could still move through it. We can even imagine an extreme case: an object that was located 13.8 billion light-years away some 13.8 billion years ago, but was moving away from us at a velocity very close to the speed of light.

That light will still propagate towards us at the speed of light, traversing 13.8 billion light-years in a timespan of 13.8 billion years. But when that light arrives at the present day, the object can be up to twice as far away: up to 27.6 billion light-years away if it moved away from us arbitrarily close to the speed of light. Even if the fabric of space didn’t change over time, there are plenty of objects we can see today that could be farther away than 13.8 billion light-years.

The only catch is that their light could travel for 13.8 billion light-years at most; how the objects move after emitting that light is irrelevant.

Light, in a vacuum, always appears to move at the same speed, the speed of light, regardless of the observer’s velocity. If a distant object emitted light and then moved quickly away from us, it could be just about as far away today as double the light-travel distance. (PIXABAY USER MELMAK)

But the fabric of space isn’t constant, either. This was the big revelation of Einstein that led him to formulate the General theory of Relativity: that neither space nor time were static or fixed, but instead formed a fabric known as spacetime, whose properties were dependent on the matter and energy present within the Universe.

If you were to take a Universe that was, on average, filled relatively evenly with some form of matter or energy — irrespective of whether it were normal matter, dark matter, photons, neutrinos, gravitational waves, black holes, dark energy, cosmic strings, or any combination thereof — you would find that the fabric of space itself is unstable: it cannot remain static and unchanging. Instead, it must either expand or contract; the great cosmic distances between objects must change over time.

First noted by Vesto Slipher back in 1917, some of the objects we observe show the spectral signatures of absorption or emission of particular atoms, ions, or molecules, but with a systematic shift towards either the red or blue end of the light spectrum. When combined with the distance measurements of Hubble, this data gave rise to the initial idea of the expanding Universe: the farther away a galaxy is, the greater its light is redshifted. (VESTO SLIPHER, (1917): PROC. AMER. PHIL. SOC., 56, 403)

Beginning in the 1910s and 1920s, observations began to confirm this picture. We discovered that the spiral and elliptical nebulae in the sky were galaxies beyond our own; we measured the distance to them; we discovered that the farther away they were, the greater their light was redshifted.

In the context of Einstein’s General Relativity, this led to a surefire conclusion: the Universe was expanding.

This is even more profound than people typically realize. The fabric of space itself does not remain constant over time, but rather expands, pushing objects that aren’t gravitationally bound together apart from one another. It’s as if individual galaxies and groups/clusters of galaxies were raisins embedded in a sea of invisible (space-like) dough, and that as the dough leavened, the raisins were pushed apart. The space between these objects expands, and that causes individual objects to appear to recede from one another.

The ‘raisin bread’ model of the expanding Universe, where relative distances increase as the space (dough) expands. The farther away any two raisin are from one another, the greater the observed redshift will be by time the light is received. The redshift-distance relation predicted by the expanding Universe is borne out in observations, and has been consistent with what’s been known all the way back since the 1920s. (NASA / WMAP SCIENCE TEAM)

This has enormous implications for the meaning behind our observations. When we observe a distant object, we don’t just see the light that it emitted, nor do we merely see the light shifted by the relative velocity of the source and the observer. Instead, we see how the expanding Universe has affected that light from the cumulative effects of the expanding space that occurred at every point along its journey.

If we want to probe the absolute limits of how far back we’re able to see, we’d look for light that was emitted as close to 13.8 billion years ago as possible, that was just arriving at our eyes today. We’d calculate, based on the light we see now:

  • how much time the light has been traveling for,
  • how the Universe has expanded between then and now,
  • what all the different forms of energy present in the Universe must be to account for it,
  • and how far away the object must be today, given everything we know about the expanding Universe.
This simplified animation shows how light redshifts and how distances between unbound objects change 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. (ROB KNOP)

We haven’t just done this for a handful of objects at this point, but for literally millions of them, ranging in distance from our own cosmic backyard out to objects more than 30 billion light-years away.

How can the objects be more than 30 billion light-years away, you ask?

It’s because the space between any two points — like us and the object we’re observing — expands with time. The farthest object we’ve ever seen has had its light travel towards us for 13.4 billion years; we’re seeing it as it was just 407 million years after the Big Bang, or 3% of the Universe’s present age. The light we observe is redshifted by about a factor of 12, as the observed light’s wavelength is 1210% as long as it was compared to when it was emitted. And after that 13.4 billion year journey, that object is now some 32.1 billion light-years away, consistent with an expanding Universe.

The most distant galaxy ever discovered in the known Universe, GN-z11, has its light come to us from 13.4 billion years ago: when the Universe was only 3% its current age: 407 million years old. The distance from this galaxy to us, taking the expanding Universe into account, is an incredible 32.1 billion light-years. (NASA, ESA, AND G. BACON (STSCI))

Based on the full suite of observations we’ve taken — measuring not just redshifts and distances of objects but also the leftover glow from the Big Bang (the cosmic microwave background), the clustering of galaxies and features in the large-scale structure of the Universe, gravitational lenses, colliding clusters of galaxies, the abundances of the light elements created before any stars were formed, etc. — we can determine what the Universe is made of, and in what ratios.

The distance/redshift relation, including the most distant objects of all, seen from their type Ia supernovae. The data strongly favors an accelerating Universe. Note how these lines are all different from one another, as they correspond to Universes made of different ingredients. (NED WRIGHT, BASED ON THE LATEST DATA FROM BETOULE ET AL.)

Today, our best estimates are that we live in a Universe made up of:

  • 0.01% radiation in the form of photons,
  • 0.1% neutrinos, which have a small but non-zero mass,
  • 4.9% normal matter, made of protons, neutrons and electrons,
  • 27% dark matter,
  • and 68% dark energy.

This fits all the data we have, and leads to a unique expansion history dating from the moment of the Big Bang. From this, we can extract one unique value for the size of the visible Universe: 46.1 billion light-years in all directions.

The size of our visible Universe (yellow), along with the amount we can reach (magenta). The limit of the visible Universe is 46.1 billion light-years, as that’s the limit of how far away an object that emitted light that would just be reaching us today would be after expanding away from us for 13.8 billion years. (E. SIEGEL, BASED ON WORK BY WIKIMEDIA COMMONS USERS AZCOLVIN 429 AND FRÉDÉRIC MICHEL)

If the limit of what we could see in a 13.8 billion year old Universe were truly 13.8 billion light-years, it would be extraordinary evidence that both General Relativity was wrong and that objects could not move from one location to a more distant location in the Universe over time. The observational evidence overwhelming indicates that objects do move, that General Relativity is correct, and that the Universe is expanding and dominated by a mix of dark matter and dark energy.

When you take the full suite of what’s known into account, we discover a Universe that began with a hot Big Bang some 13.8 billion years ago, has been expanding ever since, and whose most distant light can come to us from an object presently located 46.1 billion light-years away. The space between ourselves and the distant, unbound objects we observe continues to expand at a rate of 6.5 light-years per year at the most distant cosmic frontier. As time goes on, the distant reaches of the Universe will further recede from our grasp.

Send in your Ask Ethan questions to startswithabang at gmail dot com!

Ethan Siegel is the author of Beyond the Galaxy and Treknology. You can pre-order his third book, currently in development: the Encyclopaedia Cosmologica.


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