There's no way to Measure the Speed of Light in a Single Direction

Special relativity is one of the most strongly validated theories humanity has ever devised. It is central to everything from space travel and GPS to our electrical power grid. Central to relativity is the fact that the speed of light in a vacuum is an absolute constant. The problem is, that fact has never been proven.

When Einstein proposed the theory of relativity, it was to explain why light always had the same speed. In the late 1800s it was thought that since light travels as a wave it must be carried by some kind of invisible material known as the luminiferous aether. The reasoning was that waves require a medium, such as sound in air or water waves in water. But if the aether exists, then the observed speed of light must change as the Earth moves through the aether. But measurements to observe aether drift came up null. The speed of light appeared to be constant.

Einstein found that the problem was in assuming that space and time were absolute and the speed of light could vary. If instead, you assumed the speed of light was absolute, space and time must be affected by relative motion. It’s a radical idea, but it’s supported by every measurement of light’s constant speed.

How to measure the round-trip speed of light. Credit: Wikipedia user Krishnavedala

But several physicists have pointed out that while relativity assumes the vacuum speed of light is a universal constant, it also shows the speed can never be measured. Specifically, relativity forbids you from measuring the time it takes light to travel from point A to point B. To measure the speed of light in one direction, you’d need a synchronized stopwatch at each end, but relative motion affects the rate of your clocks relative to the speed of light. You can’t synchronize them without knowing the speed of light, which you can’t know without measuring. What you can do is use a single stopwatch to measure the round trip time from A to B back to A, and this is what every measurement of the speed of light does.

Since all the round-trip speed of light measurements give a constant result, you might figure you can just divide the time by two and call it a day. This is exactly what Einstein did. He assumed the time there and back was the same. Our experiments agree with that assumption, but they also agree with the idea that the speed of light coming towards us is ten times faster than its speed going away from us. Light doesn’t have to have a constant speed in all directions, it just has to have a constant “average” round-trip speed. Relativity still holds if the speed of light is anisotropic.

A Milne universe with anisotropic light would look uniform. Credit: Wikipedia user BenRG

If the speed of light varies with its direction of motion, then we would see the universe in a different way. When we look at distant galaxies we are looking back in time because light takes time to reach us. If distant light reached us quickly in some direction, we would see the universe in that direction as older and more expanded. The faster light reaches us, the less “back in time” we would see. Since we observe a uniform cosmos in all directions, surely that shows the speed of light is constant.

Well, not quite, as a new study shows. It turns out that if the speed of light varies with direction, so does length contraction and time dilation. The team considered the effects of anisotropic light on a simple relativistic model known as the Milne universe. It’s basically a toy universe similar in structure to the observe, but without all the matter and energy. They found that the anisotropic of light would cause anisotropic relativity effects in time dilation and cosmic expansion. These effects would cancel out the observable aspects of a varying light speed. In other words, even if the universe was anisotropic due to a varied speed of light it would still appear homogeneous.

So it seems simple cosmology isn’t able to prove Einstein’s assumption about the speed of light either. Sometimes the most basic ideas in science are the most difficult to prove.

Reference: Lewis, Geraint F., and Luke A. Barnes. “The One-Way Speed of Light and the Milne Universe.arXiv preprint arXiv:2012.12037 (2020).

4 Replies to “There's no way to Measure the Speed of Light in a Single Direction”

  1. Theoretically the speed of light is constant in a vacuum. Observationally there ain’t no such thing as a vacuum. This is evident in the fact that the light waves (actually microwaves) from the leading edge of the emissions from Pulsars (within the Milky Way) and Fast Radio Bursts (extra galactic) arrive at different times depending on wavelength. Shorter wavelengths arrive before longer wavelengths. The speed of light from these sources is proportional to wavelength.

    There are two implications. First, the Index of Refraction of the interstellar and intergalactic media is greater than 1. Second, the universe is not expanding. The Red Shift is due to tired light rather than recessional velocity.

  2. But we don’t seem to live in a Milne universe, which is 4D curved and only locally flat – there doesn’t seem to be any practical problem [“Milne model” @ Wikipedia, “Speed of light” @ Wikipedia].

    Our universe is 3D and flat as observed in cosmic background spectra, as expected from inflation.

    If the model topology is connected to a putative “Big Bang” singularity as in the image, it is moreover prohibited by inflation.

    “But if at some early time, the Universe isn’t dominated by matter or radiation, but by a form of energy inherent to space itself, you get the yellow curve. Note how this yellow curve, since it’s an exponential curve, never reaches zero in size, but only approaches it, even if you go infinitely far back in time. An inflating Universe doesn’t begin in a singularity like a matter-dominated or radiation-dominated Universe does. All we can state with certainty is that the state we call the hot Big Bang only came about after the end of inflation.”

    [“What Came First: Inflation Or The Big Bang?” @ Forbes]

  3. @roylofquist:

    That the universe is expanding is an observation, as well as well tested theory which is stronger than any single observation [“Hubble’s law” @ Wikipedia, “What Came First: Inflation Or The Big Bang?” @ Forbes].

    That a “tired light” hypothesis doesn’t work has long been known, including when it was proposed by its inventor – that hasn’t changed but become catastrophically much worse. (While at the same time expansion universes has become ever much better theory – now at generally ~1 % remaining uncertainty – so is the only game in town today.]

    “The concept was first proposed in 1929 by Fritz Zwicky, who suggested that if photons lost energy over time through collisions with other particles in a regular way, the more distant objects would appear redder than more nearby ones. Zwicky himself acknowledged that any sort of scattering of light would blur the images of distant objects more than what is seen. Additionally, the surface brightness of galaxies evolving with time, time dilation of cosmological sources, and a thermal spectrum of the cosmic microwave background have been observed—these effects should not be present if the cosmological redshift was due to any tired light scattering mechanism.[1][2][3] Despite periodic re-examination of the concept, tired light has not been supported by observational tests and remains a fringe topic in astrophysics.[4]”

    [“Tured light” @ Wikipedia]

  4. Zwicky was correct but he proposed the wrong mechanism. He proposed collisions with particles, which is incidentally how modern cosmologists explain the time dispersion of the signals from Pulsars and FRBs. However, if the retarding mechanism is field like there would be no scattering. There are a number of candidates – Zero Point Energy, Higgs Field, Faraday Effect…

    The signals from Pulsars and FRBs behave precisely as if the medium they traversed had an Index of Refraction greater than unity, unity being what a perfect vacuum would have. The shorter wavelength components of the signals arrive before the longer wavelengths. They travel at different speeds less than c. There is a formula, verified by parallax measurements, that yields the distance of a pulsar based upon the time difference of two wavelengths. It is of the same form as the formula used to calculate the distance to distant galaxies.

    You wrote: “That the universe is expanding is an observation, as well as well tested theory..”. No, it is not an observation. It is an inference based on the reddening of distant objects.

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