The Only Speed of Light That Matters

A couple weeks back, someone asked me about a Veritasium video with the provocative title “Why No One Has Measured The Speed Of Light”. Veritasium is a science popularization youtube channel, and usually a fairly good one…so it was a bit surprising to see it make a claim usually reserved for crackpots. Many, many people have measured the speed of light, including Ole Rømer all the way back in 1676. To argue otherwise seems like it demands a massive conspiracy.

Veritasium wasn’t proposing a conspiracy, though, just a technical point. Yes, many experiments have measured the speed of light. However, the speed they measure is in fact a “two-way speed”, the speed that light takes to go somewhere and then come back. They leave open the possibility that light travels differently in different directions, and only has the measured speed on average: that there are different “one-way speeds” of light.

The loophole is clearest using some of the more vivid measurements of the speed of light, timing how long it takes to bounce off a mirror and return. It’s less clear using other measurements of the speed of light, like Rømer’s. Rømer measured the speed of light using the moons of Jupiter, noticing that the time they took to orbit appeared to change based on whether Jupiter was moving towards or away from the Earth. For this measurement Rømer didn’t send any light to Jupiter…but he did have to make assumptions about Jupiter’s rotation, using it like a distant clock. Those assumptions also leave the door open to a loophole, one where the different one-way speeds of light are compensated by different speeds for distant clocks. You can watch the Veritasium video for more details about how this works, or see the wikipedia page for the mathematical details.

When we think of the speed of light as the same in all directions, in some sense we’re making a choice. We’ve chosen a convention, called the Einstein synchronization convention, that lines up distant clocks in a particular way. We didn’t have to choose that convention, though we prefer to (the math gets quite a bit more complicated if we don’t). And crucially for any such choice, it is impossible for any experiment to tell the difference.

So far, Veritasium is doing fine here. But if the video was totally fine, I wouldn’t have written this post. The technical argument is fine, but the video screws up its implications.

Near the end of the video, the host speculates whether this ambiguity is a clue. What if a deeper theory of physics could explain why we can’t tell the difference between different synchronizations? Maybe that would hint at something important.

Well, it does hint at something important, but not something new. What it hints at is that “one-way speeds” don’t matter. Not for light, or really for anything else.

Think about measuring the speed of something, anything. There are two ways to do it. One is to time it against something else, like the signal in a wire, and assume we know that speed. Veritasium shows an example of this, measuring the speed of a baseball that hits a target and sends a signal back. The other way is to send it somewhere with a clock we trust, and compare it to our clock. Each of these requires that something goes back and forth, even if it’s not the same thing each time. We can’t measure the one-way speed of anything because we’re never in two places at once. Everything we measure, every conclusion we come to about the world, rests on something “two-way”: our actions go out, our perceptions go in. Even our depth perception is an inference from our ancestors, whose experience seeing food and traveling to it calibrated our notion of distance.

Synchronization of clocks is a convention because the external world is a convention. What we have really, objectively, truly, are our perceptions and our memories. Everything else is a model we build to fill the gaps in between. Some features of that model are essential: if you change them, you no longer match our perceptions. Other features, though, are just convenience: ways we arrange the model to make it easier to use, to make it not “sound dumb”, to tell a coherent story. Synchronization is one of those things: the notion that you can compare times in distant places is convenient, but as relativity already tells us in other contexts, not necessary. It’s part of our storytelling, not an essential part of our model.

5 thoughts on “The Only Speed of Light That Matters

  1. Dimitris Papadimitriou

    During the last months, I had the opportunity to watch some of these pop- sci videos ( there are lots of them, with various degrees of popularization) and the main thing I’ve noticed is that while they’re trying to avoid seriously wrong statements, they’re choosing titles that sometimes are provocative ( to gain more views) and, as a result, they give the wrong impression to their viewers without having the intention to do so.
    In many ( not all!) of these videos there are several reoccurring misleading statements, some of them more frequent than others: e.g. the typical confusion between the Bell/ EPR quantum non locality/ non separability with the Einsteinian locality/ causality (; the former is very common, while the latter has never been violated), or the claim that a typical Schwartzschild black hole singularity is ” a point at the center of the hole” ( i.e. the confusion between spacelike and timelike singularities) and the similar claim that the infalling matter is compressed altogether in that miniscule pointlike ” thing”, and so on…
    I have not seen this Veritasium video, yet, but this topic about the speed of light reminds me some ” issues” that a philosopher ( von Reichenbach?) had written about long ago, in the previous century.

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    1. 4gravitons Post author

      Yeah, titling in general is a shady business. For articles I know how this works, most outlets let editors change titles pretty freely regardless of what the author thinks. This shouldn’t be relevant for YouTube videos but maybe there are similar pressures.

      I think some of those who confuse relativistic locality and quantum nonlocality are doing it intentionally, in that they think that the quantum kind is the “real one” and the other one is just a particle physics misnomer. I tend to find that kind of fighting over words pretty silly but eh. Of course many popularizers just don’t know or don’t clarify the difference.

      Similarly, the idea of a Schwarzchild singularity as a point is not exactly ridiculous as a first pass description, even if it isn’t really the right way to think about it in a serious general relativistic way. Certainly the most commonly used coordinate chart for the Schwarzchild metric puts the singularity at a single point, so it’s hard to teach this stuff to an undergrad (who isn’t going to really understand diffeomorphisms but can absolutely be taught about the Schwarzchild metric) without that particular “lie to children”.

      You’re right to think of Reichenbach, indeed he apparently proposed the standard parametrization for these things.

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  2. Tom

    Hello, I am not a physicist, but I was wondering: If it could be experimentally determined, without the use of clocks, that light traveled at the same speed in any given direction, would this be useful information to the field of physics? Or would it just be considered “interesting”?

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    1. 4gravitons Post author

      I mostly agree with the reddit commenter who linked you here.

      One thing that may not be obvious is that when physicists talk about “clocks” they don’t literally just mean clocks, they mean any measurement of time. The problem with synchronizing clocks is really not an experimental problem, it’s a theoretical problem, the problem of comparing different notions of time in different places. And you’re always going to have that problem, since you the person doing the measurement is always going to be sitting in one place. You will always need to have some mathematical rule for translating the time you measure where you are to the time measured elsewhere, and someone else could always just choose to use a different mathematical rule. That’s why I say in this post that it’s not just the one-way speed of light that can’t be measured, but the one-way speed of anything: perception itself is a two-way process.

      The only way to change that is to fix that mathematical rule, to say that there is only one choice allowed for translating time between different places. You can kind of do that now, just say that obviously light goes the same way in different directions, anything else makes the math really inconvenient. In practice, that’s what physicists already do. But you’re fixing the rule based on convenience, not on some experimental result.

      So if there was an experimental result that told you which mathematical rule to use to translate time between different places…well, I’m just not sure how that would work. Something that lets an experimenter be in two places at once? I don’t know whether that would be useful or “huh that’s interesting” because I have no idea what it could imply!

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  3. Kris

    I think we can measure one way speed of light :
    Imagine four spaceships flying as perfect square EFGH towards (or away from) not moving (at least relative to each other) points ABCD (could be another four spaceships), where AD is parallel to EF and distance EF equals AD. Points EG should be collinear with points AB and points FH collinear with CD. Making sure that ABCD (and EFGH) is a square is relatively easy, since 2-way speed of light is constant:We can measure (and correct, if necessary) distances BD and CA by sending light signals from B to D (and from C to A) and back (as well as distances from H to E and from H to F)Now we can measure (e.g. constantly) distance from A to G (L) and from D to H (L’) using light (laser) signal send from A to G (and reflected back to A) as well as distance from D to H. If for example at 12:00 o’clock we measure the distance from A to G equal 100,000.000001m at AIf we measure at D the distance of 100,000.000001m at 12:15, we would know that the clocks at A and D have a time difference of 15 min.If both measure exactly 100,000.000001m at 12:00, they are perfectly synchronized Please let me know if I made any wrong assumption.
    kkris1@yahoo.com
    (Sorry, I couldn’t paste my drawings here)

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