Can The Speed of Light Change? (script) (Patreon)

One of the most fundamental physics facts is that the speed of light in a vacuum is constant for all observers. But can we really be sure that the speed of light wasn’t different in the past, or perhaps in other parts of the universe? In fact, variable speed of light theories have long been used to try to explain everything from dark energy to gravity itself. Let’s explore how constant this fundamental constant really is.

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Speed is relative. Drop your smoothie on a train and it appears to fall straight down, but to me standing on the platform the smoothie falls diagonally, apparently boosted by the speed of the train. But shine a laser beam from the train and everyone observes the same speed—299,792,458 m/s in a vacuum, no matter their relative speeds.

The invariance of the speed of light is more precisely described by something called Lorentz invariance, and it’s the founding axiom of special relativity. Einstein realized that our measurements of distance and time have to be relative to the observer—they have to shift to keep the speed of light the same for everyone. This same axiom is also fundamental to general relativity, in which gravity is interpreted as a warping of the fabric of

spacetime. Both special and general relativity have been tested with extreme care and precision over and over and have never failed. More to the point, the speed of light has been measured in different reference frames and its invariance holds down to the exquisite precision of current methods.

That said, we scientists are supposed to remain simultaneously skeptical and open minded—somehow applying both mindsets to both old and new theories. In that spirit let’s ask whether the speed of light is really invariant. For example, could it change over time, or be different in different parts of the universe? There are some who believe that the very effects that relativity predicts are due to the speed of light changing, not due to changes in space and time.

Now before I start talking about what it means for the speed of light to change, I want to make it clear why many, and perhaps most physicists think that it’s not only impossible, but it’s not even meaningful to think about a variable speed of light.

The speed of light isn’t really about light. It’s the speed of any massless particle, and also the maximum speed that information can travel. It’s the speed of causality. It’s the rate at which one point in space can communicate with its neighbors, assuming no impediments. So to change the speed of light, we’d need to change something pretty fundamental about the universe—the connection between space and time.

We measure speed in terms of the amount of distance traveled per unit of time, whether that’s miles per hour or meters per second. Changing the speed of light means changing the number of meters it can travel every second. The problem with this is that our very definition of meters and of seconds are tied to the speed of light. We can think of the meter as the distance light travels in 1-over-300 million seconds. Or the second as how long it takes light to travel 300 million meters.

Einstein said that “time is what clocks measure”, which we can interpret as meaning that it’s a measure of the rate of change. One of Einstein’s thought experiments was the photon clock, in which he imagined a photon bouncing between two mirrors, with each 2-way trip indicating the tick of the clock. What happens if we slow the speed of light? The clock ticks more slowly, which means time slows.

Real clocks are made of gears or electronics which are made of atoms which are made of various quantum oscillations bound up in ways analogous to the photon clock—whether electrons communicating virtual photons with the nucleus, or quarks exchanging gluons in that nucleus. This argument applies for any object with mass—the speed of light dictates the rate of internal change, which determines the rate of the flow of time.

So if slowing light also slows time, would we even notice? Not according to pure special relativity, in which space and time are fundamentally coupled—two sides of the same coin. Changing the speed of light slows time, and moving the mirrors further apart slows time. In this picture, distance, time, and the speed of light scale together, so on our scale there’s no observable effect. The speed of light is just the unit conversion factor between our arbitrary choices of spatial and temporal units.

The only way for a change in the speed of light to do anything is if time and space both have their own fundamental units that are independent of each other. If there’s a basic smallest unit of space and a smallest unit of time, and these don’t depend on the other, then maybe changing the speed of light would change the relationship between space and time, at least on the quantum scale. Let’s imagine that this is possible and explore the consequences.

The first real “variable speed of light” theory was proposed by Robert Dicke back in 1957. Dicke was a brilliant physicist and astronomer with wide-ranging contributions, so we should at least pay attention to his musings. Dicke wondered if gravitational fields might not be due to the bending of spacetime, but instead due to the speed of light slowing down near massive objects. Remember that light changes its direction as it moves into a medium where its speed is lower—that’s exactly how lenses work. So why not gravity too? And we know that time ticks slower in a gravitational field. And we also now know that slowing the speed of light should slow time. Seems like a variable speed of light could be an elegant alternative hypothesis, no?

No. Back in 1957 there were only a few successful tests of general relativity, and some of those were consistent with either spacetime curvature or a changing speed of light.

But nowadays we know that spacetime itself must be dynamic—we’ve measured how rotating masses drag space around, and how colliding black holes generate gravitational waves, none of which work with the variable speed of light interpretation. Dicke’s idea was intriguing, but it doesn’t stand up to the latest evidence. And given that evidence, Dicke himself would surely agree.

OK, so maybe a variable speed of light doesn’t explain all of gravity. But could it still play a part? There’s one weird fact about our universe that could possibly be explained by this idea. If we look at the edge of the observable universe in that direction we see the warm, smooth gas that existed before any stars or galaxies formed. We see exactly the same in that direction, or that, or that. The universe at early times was extremely homogeneous—almost the same density and temperature everywhere. That tells us that at some point in the distant past that material had to have been in contact in order to distribute energy and settle into the same state. But the problem is, based on the observed rate of expansion of the universe, there just wasn’t time since the Big Bang for those regions to communicate with each other.

We’ve talked about this issue previously, along with the mainstream solution of cosmic inflation.

Inflation hypothesizes that at some very early time those distant regions WERE in causal contact with each other, enabling them to share energy at regular light speed and reach the same temperature. But then the universe underwent a period of extremely rapid expansion much faster than the speed of light before slowing dramatically. This threw apart regions that were close enough to be in thermal equilibrium so far apart that now it appears as if they never were.

But there’s another way to bring those distant points into causal contact—and that’s by having light just move faster in the past. This could have kept the early universe connected as it expanded and reached uniformity. Then, if light slowed down to the current much slower speed, distant regions would seem causally disconnected.

And if this story is right, it could even be that the speed of light has been gently decreasing ever since. It has been suggested that this could explain why many galaxies appear to be accelerating away from us. Since light is becoming slower it's taking longer and longer for their light to reach us, giving the appearance that they are accelerating away from us. That may sound good, but variable speed of light theories don’t have a good explanation for why lightspeed would change in the very particular ways needed to mimic both inflation and dark energy. Cosmic inflation seems a little cleaner, and is certainly better accepted.

The first effort to explain the horizon problem with a variable speed of light was by John Moffat in 1992. He proposed that the speed of light may have been 10^30 m/s in the early universe. Moffat lays out some substantial theoretical work, involving a symmetry breaking analogous to the one that separated the electromagnetic and weak forces. But in this case the broken symmetry was Lorentz invariance. Moffat’s theory preserved Lorentz invariance on relatively small scales—like across the galaxy—but allowed it to vary over cosmological distances and times. Another similar idea came from Andreas Albrecht and Joao Magueijo.

And yet another VSL model depends on the energy of light—higher energy photons move faster. Perhaps the ultra-high energy photons near the big bang did travel fast enough to connect distant points of the universe. Then, as the universe cooled, high energy photons became rare and so slowed down.  Now we absolutely have not observed speed differences for light at any energy we’ve detected, and that includes comparing the arrival times of high energy gamma ray light from gamma ray bursts with that of lower energy light from the same explosions. But maybe the effect only kicks in at the really ridiculously high energies near the big bang.

These are fun ideas, but are they testable given that VSL theories predict the same thing as more standard ideas in general relativity? Well, another way to look for changes in the speed of light is via its effects on physics. “c” appears everywhere in our laws of physics—for example in the fine structure constant, which defines the strength of electromagnetism. The formula for alpha includes the charge of the electron, the electric permittivity of the vacuum, Planck's constant, and the speed of light. We’ve talked about this important constant of nature in the past, and even about whether it may have changed over time. Well, if the speed of light has changed then you’d expect the fine structure constant to change with it. And guess what—there’s no evidence of such a change. You can see our previous episode for that lack of evidence.

None of this proves that the speed of light has never varied—it just says it can’t have varied much over the past billions of years. But the real challenge to VSL theories is how they seem to break physics.

All VSL theories break Lorentz Invariance, and Lorentz Invariance seems pretty important for the universe to make sense. Remember the example about the smoothie from the beginning of the video? In that example you and I had a different interpretation of the same event, and yet, we both would agree on every aspect that mattered, like the fact that the smoothie hits the floor at a particular location, or that it hits the floor after it's dropped rather than the other way around. The basic self consistency of the universe and the causal ordering of events is ensured under Lorentz invariance. Break it and it’s pretty easy to come up with nonsensical scenarios in which different observers have irreconcilable disagreements about the outcome of events.

A variable speed of light also breaks the fundamental charge-parity-time symmetry of the universe, in that the laws of physics look fundamentally different depending one the direction of time. We’ve discussed CPT symmetry before. This is also problematic because CPT symmetry is believed to be truly fundamental, and we have no evidence of it breaking.

There are ways around some of these objections. For example, we can imagine that the change in the speed of light is not exactly fundamental, but more akin to how that speed changes in a dense medium like water. What if the refractive index of the universe changed over time? Well, that increase in the thickness of the vacuum would have to be pretty enormous to slow light by the factor of 10^22 needed to solve the horizon problem, and it appears to affect all light-speed waves equally—all frequencies of light, as well as gravitational waves. Regular materials don’t behave like that. Still, it’s a way out. And there are some other narrow paths through the dense network of refutations. However you need to be pretty committed to VSL theories to find them.

Currently there’s no evidence that the speed of light varies in a fundamental way, and it may be that it’s not even a meaningful concept. Although that latter point depends on an understanding of the quantum nature of space and time and their relationship that we don’t yet have. It’s absolutely worth going back and questioning the founding axioms of even our most successful theories, as long as we keep in mind that any new theory is going to have to do just as well or better in all of the predictions of the old theory. That’s a tall order when you’re trying to break relativity, which has such deep internal consistency and is so powerfully predictive. But it’s not a final theory due to its clash with quantum mechanics, so do let’s keep questioning it. Including whether the cosmic speed limit is fixed, or if we can change how fast information travels though spacetime.