8 mins read 27 Jan 2021

The One-Way Speed of Light

When Einstein developed his Special Theory of Relativity, he assumed that light travelled at the same speed between two points no matter which direction it was moving in. But is that really the case, and would the Universe look any different if it were not?

Although we assume that the speed of light is equal in all directions, this has not been shown to be true by experiment. We have only ever measured the round-trip speed of light. Could it be that the speed of light is anisotropic? Credit: GETTY

You probably know something about the speed of light. For one thing, you are very likely aware that it’s fast, really fast, and that nothing in the Universe can travel any faster. But did you know that the speed of light might vary depending on which direction it is travelling in? And even more astonishingly, that we may never be able to confirm whether it does?

Researchers Prof Geraint Lewis, of the University of Sydney, and Dr Luke Barnes, based at Western Sydney University, have looked at how we define and measure the speed of light in the Universe, and whether differences related to direction of travel would affect our view of the cosmos. Both are well-qualified to answer deep philosophical questions in cosmology, having authored several books and scientific papers together including 2020’s The Cosmic Revolutionary’s Handbook.

If you were to shine a torch at a distant mirror and use an accurate clock to time how long the light took to return to you, it is simple enough to calculate the speed at which it was travelling. For at least a couple of hundred years we’ve known that the speed of light, commonly denoted c, is about one billion kilometres per hour.

But is it possible that the light travelled more slowly to the mirror than it did on the way back? For example, if the total trip time was 10 seconds, could the light have taken 8 seconds to travel to the mirror and only 2 seconds to return? Or the full 10 seconds to travel to the mirror, and been reflected back instantaneously? And is this something we could measure?

Using a model of the Universe that is consistent with Einstein’s special relativity, the researchers calculated what effect changing the speed of light in one direction would have on our view of the night sky. To keep the round-trip speed at c, any increase in the speed in one direction must be countered by a decrease in the opposite direction. But even infinite one-way speeds are consistent with the laws of physics.

What they found is that even if light were able to travel instantaneously in one direction, we would have no way of knowing it. The effects of time dilation would precisely cancel out any differences we would expect to see in the sky because of differing one-way light speeds.

Wait, what?

Let me explain. And we'll begin with a bit of background science.

It's All Relative

Einstein showed that the flow of time is different for different observers travelling at different speeds. Despite the counter-intuitive nature of this discovery, it has been proven time and again, including by GPS satellites. Credit: andrey_l/Shutterstock

It was Einstein that pointed out how light works during his annus mirabilis in 1905, the year in which he transformed our understanding of time, speed, mass and energy forever. His paper titled ‘On the Electrodynamics of Moving Bodies’, the third he released that year, challenged the notion that space and time were absolute and universal, like a stage on which we all act out our parts.

Einstein connected the concepts of space and time and showed that how we perceive them depends on how we are moving through them. Two people moving with respect to each other experience time and space differently. There is no universal time, no way of synchronising clocks, in Einstein’s universe.

Without a way to synchronise clocks, it is impossible to measure the speed of light in one direction. To demonstrate why, consider a simple experiment where we setup a test rig to shine a light from one end to the other. Clocks are placed at either end of the rig so that we can check the start time and end time. Knowing the length of the rig and the time it takes the light to travel from one end to the other, we can calculate its speed.

It sounds easy enough, doesn't it? But here lies the problem. Although we carefully synchronise the two clocks before the experiment, the very act of moving them to each end of the test rig will undo our good work. While they are moving, the rate at which time passes will be slightly different for each clock. This is an effect known as time dilation, and it is very real and measurable. GPS satellites need to account for this effect every day.

Any variation on this experiment will have the same complication. We just cannot measure the speed of light in one direction because relativity prevents us from maintaining synchronised clocks. The result is that the speed of light c is really the average speed over a round-trip journey, and that we cannot be certain that the speed is the same in both directions.

Toy Universes

Modelling the universe using mathematics allows astronomers to make predictions and to explain observations. The Milne universe is a special case of the Friedmann–Robertson–Walker (FRW) model which is sometimes called the standard model of modern cosmology.

To study the implications of this on our view of the Universe, Prof Lewis and Dr Barnes used an idealised model universe called the Milne universe that allowed them to perform the necessary math. The Milne universe is a special case of another, more complex, model that forms the basis of our current understanding of the cosmos. Prof Lewis explained the advantages of using the Milne universe.

“We used the Milne universe as it is empty space, no matter or energy, and we can easily map this onto the other empty space, namely the flat spacetime of Einstein’s special theory of relativity. Considering general universes – with matter and stuff – the picture becomes more complex as there is a gravitational influence on clocks which modifies their synchronization.”

As it happens, Milne universes are excellent tools for an analysis like this, exhibiting many of the properties of our own cosmos without the need for the complexity that general relativity brings. With their model universe the researchers could abandon Einstein’s convention for clock synchronisation, where light travels at the speed c in every direction, and work through the calculations describing how we then perceive the Universe.

Our View of the Universe

When we look at the distant Universe, we see something that is remarkable. At large enough scales, it looks the same at every location, but it also looks the same in every direction. These two properties are known as homogeneity and isotropy. Our Universe need not have been homogeneous and isotropic but it appears to be so, something we refer to as the cosmological principle.

We have deduced that the distribution of matter in the Universe obeys the cosmological principle, in part, through our observations of distant galaxies and of the cosmic microwave background (CMB), the leftover radiation from the Big Bang. The cosmological principle was central to Milne’s development of his model universe.

Now, if the speed of light were different depending on its direction of travel, that would mean that the speed of light itself would be anisotropic. Shouldn’t we be able to see some evidence on this imprinted on our view of the sky? When we look at opposite sides of the sky, shouldn’t we see some differences in the distributions of young galaxies, and in the CMB itself?

And finally, we come to the results of this research. The conclusion drawn by Prof Lewis and Dr Barnes was that even if the speed of light were anisotropic, observers in a Milne universe would still be presented with an isotropic view of the distant cosmos – just as we are. The effects of time dilation compensate for other effects precisely, ensuring that we would see no difference in the sky.

This is a concept that has been and continues to be challenged by some physicists around the world, who argue that the speed of light must be the same in both directions. “But it does not have to be!” said Prof Lewis.

“Even though the one-way speed of light is not experimentally measurable, and we sleep well at night thinking it is isotropic, that does not mean that we should not be prepared for the possibility that some future experiment shows us that it is not.”

The good news is that Einstein’s relativity does not break down even without his innocuous assumption that the speed of light is isotropic. Thinking about what this implies on the nature of time and space is mind-bending, but it is not inconsistent with our understanding of cosmology generally.

What research like this does do though is help us build a more complete picture of the reality underlying our existence. And what a wonderful existence it is.

Video Credit: Veritasium (YouTube)

The paper appears on the arXiv preprint server...