I’ve been to the top of Santiago Peak, one of the mountains mentioned in the article. Its got a handful of big line of site radio towers with microwave tx/rx on it [1]. These peaks would probably be a good candidate for laser-based radio transmission one day. I find that kind of ironic given the fact that Michelson tested with light between 1922 to 1931!
>The proper terminology is of course “velocity of light”, but most non-physics people conventionally use “speed of light”, which I shall do so from this point forward.
That's not right, velocity is a vector (a magnitude and a direction) and speed is a scalar (just a magnitude). The speed of light, c, is a scalar: in fact, one of the biggest things that Michelson showed is that it is the same in every direction! (If the speed of light was anisotropic then I think c would be a tensor).
I don't think I've ever heard anybody say "the velocity of light." I wonder where that came from.
Fun fact: The speed of light is only constant by convention. There's a nice creationist paper where they try to twist physics into a pretzel in order to make it fit the biblical narrative, using a convention where the speed of infalling light rays is infinite, but the speed of outgoing ones only c/2.
Of course, any such attempt will eventually fail due to invariants that are independent of convention, such as the age of the universe as measured by an observer following the Hubble flow.
One can't help but be impressed at least a little bit by the ingenuity of it all, though...
"Fun fact: The speed of light is only constant by convention."
Well, the speed of light through a non-vacuum isn't the same as any medium will slow it to some extent, but the speed of light in a vacuum is the definition of "c" and as such, that IS a constant and invariant.
I'm not talking about a metric over space, but rather a metric over spacetime, if that's what you mean. I would consider that to encode the space/time decomposition. My differential geometry sucks, but I thought you could write general relativity in a coordinate free manner that specifically doesn't rely on strong coordinate choices like you're talking about.
I thought you could write general relativity in a coordinate free manner that specifically doesn't rely on strong coordinate choices
Indeed. But even before you start messing with the formalism, the metric alone cannot be used to define a speed as 4-velocities are normalized. You need to decompose your tangent space into timelike and spacelike subspaces so you can have a dx and a dt.
Investigating which axioms of your theory can be weakened whithout affecting its predictions seems worthwhile to me even if it's useless from a practical perspective.
>The speed of light is only constant by convention.
I don't think that's true. If someone wrote a paper where the speed of light is different in one direction than another, then that's in clear contradiction with experiments. Yes, there are some legitimate searches for anisotropy in flat space, but they have all come up negative. So, I wouldn't say that it's "constant by convention."
You can make a model where the speed of light is relative and be totally consistent with all the scientific observations. That model would be more complicated though.
I can think of two things that you might be alluding to, models that have a parameter that is named "the speed of light," but that does not actually correspond to the speed of light, and models that predict phenomena beyond what current experiments have detected. In the first case, anything that is in line with experiment must predict a constant speed of light, even if they do it with non-constant parameters, perhaps even parameters named c. In the second case, sure, but they aren't supported by experiments.
I have also seen many cranks in physics forums claim special relativity is largely an artifact due to the convention of Einstein synchronization, which they claim is falsehood, as this convention adopt the equivalence between "one-way" and "two-way" speed of light as an axiom, and special relativity would be the natural consequence. But there's no reason to accept that, without accepting it, all the arguments for time dilation, etc, collapse, thus special relativity is invalid, then they return to non-relativistic classical mechanics and Galileo transformation.
Not a mathematician or physicist, many things are not right in those arguments, I don't know what to say.
You can safely ignore that: Relativity and classical mechanics make different predictions, and we've done the experiments.
But if you travel into the weeds, a constant speed of light is not the only way to arrive at those predictions: In the extreme case, you could make the speed of light infinite in one direction if you slow it down to c/2 in the opposite direction. We don't do that because we like symmetries, and having light jump instantly from the surface of the sun to hit your head, then 'crawl' towards a mirror only to make an instantaneous jump into your eye seems rather weird...
I accept the findings of those experiments, such as [1]. But if you are a crank, you can always come up with conspiracy theories which claim "The Experiment X" back in the 1930s disprove it but is suppressed by the establishment. I used to read those posts as entertainment, but I stopped since then, as it stopped being fun after a month or so.
> But if you travel into the weeds, a constant speed of light is not the only way to arrive at those predictions
I think many major subjects of natural science have a "catch" like this. What is being written in popular science and most textbooks is merely a caricature of the subject, far from the full picture, but is considered "correct enough" to be a useful mental model (or physical model) for public consumption. For a simple example, an electric circuit is inherently an electromagnetic phenomenon, yet the fairy tale of "the flow of electron" is commonly used, it's an incomplete and flawed model even at DC. We use it because most people, myself included, are incapable of thinking the physical picture of vector calculus and solve PDE mentally, let alone Quantum Field Theory, not to mention the "truth" is only sometimes relevant and useful.
Thus, if someone wants to engage in denialism or create FUD, one could just write something that is largely relevant but out-of-context, and say "you are being fooled, everything you know is wrong"! I suspect many pseudoscientific subjects, like the anti-vax movement or crank physics, frequency use this technique (or fell into it).
Also, I once saw a LessWrong post that hypothesized: engineers are more likely to become cranks - because they are knowledgeable enough to spot a flaw in a physical model commonly used in the industry, and realize they are being fooled by thinking critically, but often they are completely unaware of the underlying history or context of the physics. I don't have data, but I definitely have seen something like this. I once saw a website by an RF engineer that claims GR is false, and built his own version using the ideas from antenna theory...
By saying speed of light, you make the assumption it is the same in any direction or reference frame. This was not known to be true, and is still the subject of some question, hence the more modern experiments measuring the speed in a fixed frame to compare to other frames.
For example, what is the speed of a bullet? It depends on the observer (as does velocity, but velocity is a more accurate thing to measure for this reason).
It so far is experimentally true that the velocity of light has the same magnitude (up to experimental error) in any frame, which was a tremendously crazy result at first, so much so that it forced mankind to give up the notion of constant flow of time, and it forces space and time to "rotate" into each other in a weird manner called space-time.
So the velocity of light is the proper term to use in an experiment.
>For example, what is the speed of a bullet? It depends on the observer (as does velocity, but velocity is a more accurate thing to measure for this reason).
That sentence doesn't make sense to me, velocity is even more sensitive to coordinate change than speed. If you rotate your coordinate system, all the velocities will change but speeds will stay the same. The phrase used in the article was "the velocity of light," which was known to be wrong even back then because light has a different velocity depending on which way it is going.
But this proves the point that speed should be used. C is the theorized speed of light in all frames. The experimental velocities of light also exist but that shouldn't be what we call C.
This doesn't make any sense. If there is an oddity its in saying "THE speed of light." THE is what makes it singular and begs the question "in what direction?" The answer is in any direction. But that doesn't mean direction is not important. If somebody asks you for THE velocity that is a nonsense question. If somebody asks you for A velocity they are asking you for the speed in each direction. Even in 1D, where the units of velocity and speed are the same, these are still not the same concepts because velocity can be negative to signify the direction of "backwards" so there are two possible velocities of light even in 1D.
I checked out one of the links [0], which lead to an article presumably by the same author, with this accompanying picture of a plaque installed at the site of measurement on Mount Wilson [1]. It clearly says velocity of light - so that might have been where the author got it from.
33 comments
[ 3.0 ms ] story [ 21.0 ms ] thread[1] https://en.m.wikipedia.org/wiki/Santiago_Peak#Radio_communic...
That's not right, velocity is a vector (a magnitude and a direction) and speed is a scalar (just a magnitude). The speed of light, c, is a scalar: in fact, one of the biggest things that Michelson showed is that it is the same in every direction! (If the speed of light was anisotropic then I think c would be a tensor).
I don't think I've ever heard anybody say "the velocity of light." I wonder where that came from.
Most likely, it’s a form of linguistic hypercorrection: https://en.wikipedia.org/wiki/Hypercorrection
Of course, any such attempt will eventually fail due to invariants that are independent of convention, such as the age of the universe as measured by an observer following the Hubble flow.
One can't help but be impressed at least a little bit by the ingenuity of it all, though...
edit: cf https://en.wikipedia.org/wiki/One-way_speed_of_light
Well, the speed of light through a non-vacuum isn't the same as any medium will slow it to some extent, but the speed of light in a vacuum is the definition of "c" and as such, that IS a constant and invariant.
We do that because we want "the statements of the natural laws [to be] as simple as possible" (Poincaré), but it's not the only way to do it...
Indeed. But even before you start messing with the formalism, the metric alone cannot be used to define a speed as 4-velocities are normalized. You need to decompose your tangent space into timelike and spacelike subspaces so you can have a dx and a dt.
I don't think that's true. If someone wrote a paper where the speed of light is different in one direction than another, then that's in clear contradiction with experiments. Yes, there are some legitimate searches for anisotropy in flat space, but they have all come up negative. So, I wouldn't say that it's "constant by convention."
In any case, the speed of light is constant.
Not a mathematician or physicist, many things are not right in those arguments, I don't know what to say.
But if you travel into the weeds, a constant speed of light is not the only way to arrive at those predictions: In the extreme case, you could make the speed of light infinite in one direction if you slow it down to c/2 in the opposite direction. We don't do that because we like symmetries, and having light jump instantly from the surface of the sun to hit your head, then 'crawl' towards a mirror only to make an instantaneous jump into your eye seems rather weird...
I accept the findings of those experiments, such as [1]. But if you are a crank, you can always come up with conspiracy theories which claim "The Experiment X" back in the 1930s disprove it but is suppressed by the establishment. I used to read those posts as entertainment, but I stopped since then, as it stopped being fun after a month or so.
> But if you travel into the weeds, a constant speed of light is not the only way to arrive at those predictions
I think many major subjects of natural science have a "catch" like this. What is being written in popular science and most textbooks is merely a caricature of the subject, far from the full picture, but is considered "correct enough" to be a useful mental model (or physical model) for public consumption. For a simple example, an electric circuit is inherently an electromagnetic phenomenon, yet the fairy tale of "the flow of electron" is commonly used, it's an incomplete and flawed model even at DC. We use it because most people, myself included, are incapable of thinking the physical picture of vector calculus and solve PDE mentally, let alone Quantum Field Theory, not to mention the "truth" is only sometimes relevant and useful.
Thus, if someone wants to engage in denialism or create FUD, one could just write something that is largely relevant but out-of-context, and say "you are being fooled, everything you know is wrong"! I suspect many pseudoscientific subjects, like the anti-vax movement or crank physics, frequency use this technique (or fell into it).
Also, I once saw a LessWrong post that hypothesized: engineers are more likely to become cranks - because they are knowledgeable enough to spot a flaw in a physical model commonly used in the industry, and realize they are being fooled by thinking critically, but often they are completely unaware of the underlying history or context of the physics. I don't have data, but I definitely have seen something like this. I once saw a website by an RF engineer that claims GR is false, and built his own version using the ideas from antenna theory...
[1] https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_exper...
For example, what is the speed of a bullet? It depends on the observer (as does velocity, but velocity is a more accurate thing to measure for this reason).
It so far is experimentally true that the velocity of light has the same magnitude (up to experimental error) in any frame, which was a tremendously crazy result at first, so much so that it forced mankind to give up the notion of constant flow of time, and it forces space and time to "rotate" into each other in a weird manner called space-time.
So the velocity of light is the proper term to use in an experiment.
That sentence doesn't make sense to me, velocity is even more sensitive to coordinate change than speed. If you rotate your coordinate system, all the velocities will change but speeds will stay the same. The phrase used in the article was "the velocity of light," which was known to be wrong even back then because light has a different velocity depending on which way it is going.
[0] https://www.otherhand.org/home-page/physics/historical-speed...
[1] https://www.otherhand.org/wp-content/uploads/2012/04/Mt-Wils...
Cue