Four myths about superluminal expansion dispelled
My 13 year old son once asked me this question: “if you took a spaceship far enough out into the universe, would you come back to where you started?”
Truthfully, I said nobody knows, but it also occurred to me that even if the universe were spatially closed like the surface of the Earth, it might be expanding so quickly that even traveling near the speed of light, your spaceship would never come back to where it started.
Think of the universe as the surface of a balloon blowing up. Stars and galaxies dot its surface. The farther apart two galaxies are; the faster they recede from one another. The expansion is so rapid points far enough away from one another are expanding apart faster than the speed of light. As you travel away from your home galaxy at near the speed of light, space in front of you that is far enough away is actually receding from you faster than you can reach it. That means that you will never reach galaxies beyond a certain distance from you.
Or would you?
It turns out that the answer is more complex than my initial intuition would suppose.
The Hubble sphere, named after Edwin Hubble, who discovered the expansion of the universe back in the 1920s, is the sphere beyond which galaxies are receding away from us faster than light.
We know that galaxies are almost all receding away from us because their light is redder than it should be. And we know what frequency that light is supposed to be because certain elements have telltale spectra called absorption or, their inverse, emission spectra. When we examine the light at different frequencies, we can see where there is more or less light. Based on our knowledge of how the elements in stars and gases behave, we know when and by how much that light has been shifted to higher frequencies (blue shift) or lower frequencies (red shift). This is called spectroscopy.
Misconceptions and easily misinterpreted statements have appeared in many popular science books and articles as well as even scientific papers concerning the Hubble sphere and the “observable” universe. One of the most common is about whether objects receding faster than the speed of light (outside the Hubble sphere) are visible or not. Indeed, they are. Unlike the event horizon, objects outside our Hubble sphere can influence those inside it and vice versa.
There are four important regions of the universe that concern us here. The first is the aforementioned Hubble sphere. The next is the particle horizon. This is the distance that light emerging at the Big Bang could have reached by a time after the the Big Bang, such as the present day. The third is the event horizon. This is the region from which light can reach us for all time from the Big Bang to infinite time. And lastly there is our past light cone which contains every point in the universe from which light could conceivably have reached us going back to the Big Bang to the present day.
Unlike the particle horizon and the event horizon, the Hubble sphere is not a horizon, meaning that it is not a region of space where we cannot see beyond it. (The word “horizon” here means exactly what it does on the two dimensional surface of the Earth, but in 3 spatial dimensions. It is a region we can see up to but not beyond.)
Although the Hubble sphere defines the transition from objects receding slower than light (subluminal) and those receding faster (superluminal), the redshift of those objects is not infinite as it would be at the event horizon of a black hole. Rather it is about 1.46 or 146% above the natural wavelengths of the light.
This does not violate special relativity because the motion is not in any observer’s inertial reference frame. In other words, no observer ever overtakes a light beam and all observers measure the speed of light to be the same.
When objects that are outside our Hubble sphere emit light, that light moves towards us at the speed of light but because the recession velocity is faster than light the total velocity of the light is away from us. But, because the Hubble sphere increases its size over time it overtakes that light. The light then suddenly shifts from moving away from us to moving towards us.
Another way to look at this is to use our past light cone as a guide. This is a four dimensional cone containing the region of spacetime from which light can have reached us from anywhere in the universe at the present moment. This light cone is about 46 billion light years wide and constitutes the “observable” universe.
If you look at a diagram of the intersection of our past light cone with the Hubble sphere, it starts out going into the past as being entirely within the Hubble sphere but once we get to about 10 billion years ago it becomes larger than the Hubble sphere at that time. Light emitted more than 10 billion years ago that we see today comes from galaxies that were actually receding from us faster than the speed of light at the time.
Thus, it isn’t as if the light came from galaxies that were moving away subluminally, emitted light, and then started receding superluminally. No, they were superluminally receding at the time, but their light entered the Hubble sphere some time after it was emitted and so became part of our night sky.
In this image, if a galaxy in the white space that is below the yellow line of the past light cone but outside the green shaded Hubble sphere emitted light towards us, it would still reach us because at some point that light would intersect the Hubble sphere. Only light that is beyond the event horizon has infinite redshift and must be invisible for all time.
With this introduction, let’s take a deeper look at four myths about superluminal recession:
Myth #1: Objects can’t recede faster than the speed of light
We have already talked about why objects can recede faster than the speed of light without violating special relativity. Let’s go a little deeper. Special relativity applies only to relative motion of inertial frames. In other words, if two observers are in constant relative motion with respect to one another, experiencing no forces, then their measurement of relative motion cannot exceed the speed of light. Moreover, neither one can measure the speed of light in vacuum of a beam emitted from the other as being anything other than the constant speed of light. From these ideas, all of special relativity’s weird predictions about time dilation arise, including the famous twins paradox.
In an expanding universe, however, we are talking about non-inertial frames where observers are not moving in space, rather space is expanding. Thus, they perceive themselves getting farther apart because distance itself is changing. Special relativity has no language to describe this situation and we have to go to general relativity. While light beams obey special relativity locally, over large distances in the universe, they obey general relativity. And while the redshift of that light can arise from motion through space, the redshift we observe from distant galaxies actually arises from the expansion of space itself not motion in space.
Because of this, the redshift that we perceive does not obey the law of special relativity and does not obey what you would normally see if an object were moving at or above the speed of light. Without understanding this, Hubble originally got his velocity calculations wrong. He thought that galaxies were actually moving away from us in space. They were not. If that were so, anything moving at the speed of light away from us would have to have infinite redshift and superluminal redshift would be meaningless.
For many years, up until about the ‘90’s, the difference between special and general relativity’s redshifts hadn’t mattered because observations were not deep enough into space. The redshifts are similar for objects that are closer but diverge significantly for objects that are tens of billions of light years away. Nowadays, we routinely observe objects with redshifts above 1.5 (150% above nominal wavelength) where recession velocity is always superluminal and the special relativity formula fails.
Myth #2: Superluminal expansion only occurs in inflationary theory
Inflation is the theory that in the early universe the universe expanded at a much faster rate than it does now. A misleading term for inflation is “superluminal” expansion or expansion faster than the speed of light, as if that is unusual. In our universe, however, where recession velocity is purely a function of distance any expansion has superluminal velocities. In addition, during inflationary periods there was a Hubble sphere as well. The only difference is that in inflation the Hubble constant that determines the velocity of expansion versus distance was much larger than it is now. The Hubble sphere was consequently much smaller.
If exponential expansion continued to the end of time the Hubble sphere would eventually be coincident with the event horizon. Thus, you would not be able to see objects outside the Hubble sphere a very long time after the Big Bang. In an ordinary inflationary theory, once inflation stops light that exited the Hubble sphere can reenter it however. Therefore, the Hubble sphere is not a horizon even in inflationary theory.
If inflation caused all distance regimes, down to the Planck length, to expand faster than the speed of light one might justifiably call it superluminal expansion. In this case, the Hubble sphere is the size of the Planck length. Ordinary inflationary theory, however, is just “faster expansion”.
Myth #3: Galaxies receding faster than the speed of light exist but we can’t see them
Occasionally, you see in popular books and even from scientists that even though galaxies can recede from us faster than light, we cannot see them. This is completely false. Let’s go deeper into that.
The speed of photons coming towards us is not the speed of light in vacuum, as it would be in a non-expanding universe. Rather it is the recession velocity minus the speed of light. This odd return to Newtonian thinking is because while light propagates at the speed of light in space always, when space is expanding, it is like the light is moving on a treadmill. If that expansion is superluminal, then the light is indeed moving away from us.
This is similar to the idea of a rocket traveling to the edge of the universe (to see if it comes back to where it started). The rocket would be traveling as fast as it can, but the universe’s expansion would cause it to be moving backwards from its distant goal.
It seems that in this case there is no way to see this light, but that is not so because the Hubble sphere itself also recedes. (This is true whether the universe’s expansion is accelerating or decelerating.) As long as the Hubble sphere recedes faster than the photons immediately outside it, we can see those distant galaxies.
The reason it recedes is because Hubble’s constant that governs the velocity with distance decreases with time. The slowing rate of expansion with distance allows the Hubble sphere to overtake photons just outside it. If this were not the case, the Hubble sphere would be coincident with our event horizon.
For proof of this, hundreds of galaxies with redshifts above 1.46 have been observed. The highest redshift observed so far is GN-z11 in Ursa Major at 11.1 and at least five galaxies with redshifts above 8 have been observed.
Our particle horizon determines how far we can see not the Hubble sphere. And theoretically, we should be able to see formations all the way back to the Cosmic Microwave Background (CMB) at 1100 redshift. Points where the CMB was emitted are currently receding at 3.2 times the speed of light or “c” but at the time of emission their speed was a whopping 58c!
Myth #4: We don’t know if general relativity is a good description of cosmic redshift
Of course, you could say that any of the observed redshifts might be values in a special relativistic model where all recession speeds are subluminal. In other words, we have no way of corroborating the velocities (or distances) of distant galaxies other than redshift and our models of the universe based on general relativity.
This is also false.
Quite a few observations rule out a special relativistic interpretation of cosmic redshift (which would rule out superluminal recession speeds). The main one comes from what are called Type Ia Supernovae. These give us a good way to measure time dilation, providing a standard clock by which to measure relativistic effects. These supernovae provide what are called “light curves” which are timed events such as 80% or 60% maximum intensity. From these events, we can examine the effects of time dilation in both a special and general relativistic theory. For us on Earth, we find that these supernovae events take longer than they would for a local observer. Measurements of this time dilation are consistent with the general relativistic picture but not with special relativity.
Another test you can do with these supernovae is looking at the magnitude (brightness in standard candles) of the supernovae. The magnitude is of course related to distance and hence a good measure for interpreting the velocity of the receding galaxy. It turns out that if you interpret the magnitude using special relativity you end up far, far off from the observed value of redshift and vice versa. General relativity provides a very good match.
Even using so-called “tired light” models to account for these effects in a steady state universe have so far failed to provide the elegant solution that general relativity provides. One issue is that when we compare the magnitude of light from distant objects to their size we find that the size is larger than the magnitude because of the expansion of the universe. Basically, because the object is receding while emitting light, its size is a function of where it was when it began emitting, while its magnitude is a function of both each photon having to travel a little farther than the previous one and losing energy to the expansion of the universe.
By the 1990s, tired light models had failed too many tests to remain viable.
Conclusion
Increasingly we are learning that superluminal speeds are a regular feature of general relativity. Some would, however, prefer not to talk about velocity at all as an observable because it invariably depends on what model you are using. While special relativity is a poor model of cosmic redshift, there are several alternative general relativistic models, each of which predicts slightly different velocities for a given observed redshift. Be this as it may, there are other observables that corroborate our interpretation of velocity and distance. Distance is, unfortunately, something of a confusing subject because it depends on if we are talking about the distance light traveled to get here or are we talking about the distance at one particular time? For most observations we are interested in the distance light traveled, but when talking about recession velocity we care about distance at one time.
As for my son’s question, we may never know, although if human beings ever learn to warp space ourselves, we may be able to create rockets that are superluminal and explore beyond what we can ever see.
Davis, Tamara M., and Charles H. Lineweaver. “Expanding confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe.” Publications of the Astronomical Society of Australia 21.1 (2004): 97–109.