Science Sundays with John Duffield: Speed of Light.

Last week I was telling you why time travel is science fiction. It’s because clocks don’t literally measure the flow of time. What they really do is clock up some kind of regular cyclic motion and show a cumulative display that we call the time. That sounds like it’s no big deal. But it is. And it’s a whopper.

You’ll know about gravitational time dilation. Clocks go slower when they’re lower. We allow for this in GPS, and it’s even detectable in a lab. See this interview with David Wineland of NIST: “if one clock in one lab is 30cm higher than the clock in the other lab, we can see the difference in the rates they run at”. But what’s the problem? The problem is he’s talking about optical clocks, and when a clock goes slower it’s because the regular cyclic motion inside that clock is going slower. So what sort of regular cyclic motion might you find inside an optical clock? The motion of cogs? The motion of a quartz crystal? No. The motion of light. And the whopper is this: the speed of light is not constant.

That goes against the grain of everything you’ve heard, doesn’t it? And it goes against the grain of what Einstein said, doesn’t it? No it doesn’t. Einstein started with the constant speed of light in 1905 when he was doing special relativity. But check this out:

1911: “If we call the velocity of light at the origin of coordinates c₀, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = c₀(1 + Φ/c²)”.

1912: “On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential”.

1913: “I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis”.

1915: “the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned”.

1916: “In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position”.

That’s Einstein talking about the speed of light varying in a gravitational field. But if you ask around about all this, some will brush it off by pointing to the word velocity. They’ll say “It’s a vector quantity my boy. It’s speed and direction. The velocity changes because the direction changes”. Guess what? That’s wrong. Go back to the original German, and what Einstein actually said was that a curvature of rays of light can only take place when die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert. That translates to the propagation speed of the light with the place varies. The word “velocity” in the English translations was the common usage, as in “high velocity bullet”. This is crystal clear because Einstein referred to c which is the speed of light, and to “one of the two fundamental assumptions”. That’s the special relativity postulate of the constant speed of light. Have a read of Ned Wright’s Deflection and Delay of Light and note this: “In a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the light”. Light doesn’t curve because it curves, and it doesn’t curve because spacetime is curved. Einstein never said that. It curves because the speed of light varies with position. Like a car veers when it encounters mud at the side of the road.

But those brush-off guys will dismiss this like they’re crazy. Do you want to see just how crazy? In relativity, we use an idealised optical clock called the parallel-mirror light-clock. It’s employed in the simple inference of time dilation due to relative velocity. OK, imagine we use two parallel-mirror light-clocks instead of the NIST optical clocks to demonstrate gravitational time dilation. Let’s exaggerate a little to make it more obvious. What you’d see is this:

parallel

Image credit: Brian McPherson

 

Those two light pulses aren’t going at the same speed. You’d have to be crazy to say they were. But those crazy guys do. And do you know what else is crazy? Check out the NIST caesium fountain clock. It’s used to define the second, like so:

“Since 1967, the second has been defined to be the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom”.

See that mention of radiation? That’s light. Some will say there’s a peak frequency which is found and measured by the detector. But note that frequency is defined as cycles per second, and the second isn’t defined yet. So what the detector effectively does is count incoming microwaves. When it gets to 9,192,631,770, that’s a second. After that, the frequency is 9,192,631,770 Hertz by definition. Then we use the second to define the metre, like so:

“Since 1983 the metre has been defined as the distance travelled by light in vacuum in 1⁄299,792,458th of a second”.

We use the motion of light to define the second and the metre. And what do we use them for? To measure the motion of light! That’s why we always measure the speed of light to be 299,792,458 m/s. It doesn’t matter what speed it’s going, that’s always going to be the answer.

But as far as those crazy guys are concerned, to hell with that. To hell with the wave nature of matter too. To hell with the coordinate speed of light varying in a gravitational field. To hell with the Shapiro delay. And to hell with Einstein. They’ll just tell you about time travel and the Goldilocks multiverse, and that the speed of light is constant. But now you know to narrow your eyes and turn your bullshit detectors to max.

Because now you know it isn’t.

13 comments on “Science Sundays with John Duffield: Speed of Light.

  1. Simon Roberts
    October 6, 2013 at 1:35 pm #

    I always suspected that it was cobblers. Thanks.

  2. duffieldjohn
    October 7, 2013 at 7:37 am #

    My pleasure Simon. This paper is worth a look: http://arxiv.org/abs/0705.4507 . Jo Magueijo and John Moffat are also mentioned in this Wikipedia article: http://en.wikipedia.org/wiki/Variable_speed_of_light . It refers to Einstein in 1911, but not later.

  3. Gareth
    October 9, 2013 at 9:19 pm #

    I don’t think you are saying anything surprising here. In Special Relativity (SR) the speed of light (in empty space) is a constant (c) in any inertial reference frame (IRF) . This basically means the speed as measured by any observer who is floating in space free from any forces, however fast he is moving relative to other freely floating observers.

    In General Relativity (GR) this is still is true, but gravity is not seen as a “force”, so that observers in free fall under gravity are regarded as IRFs.

    So in SR IRFs move at constant velocity with respect to each other, but in GR they don’t have to. (They could for example be in orbit around different stars).

    If a beam of light passes near a massive object (planet, star, black hole) its path will curve towards the mass.

    If I observe this from a long distance away I will see the light slowing down as it nears the mass. But if there are observers in free fall along the path of the beam, each will measure the speed of the light, at every point on the path, to be c. That is what is meant by saying the speed of light is constant in GR. And yes that explains why their clocks go slower than mine.

    But all this is standard GR as I learned it nearly 30 years ago. Who exactly are these “crazy guys” who say anything different?

    As for using the speed of light to define the second and the meter. Yes, as currently defined the speed of light has to be exactly 299,792,458 m/s. That does not change the fact that when Michelson and Morley measured the speed of light in 1887 they found it to be constant. In those days a meter was the length of a particular piece of metal and a second was a fraction of the time it takes for the Earth to rotate. You can use any units you like, the speed of light will still be constant.

    This is a common process in physics. For example James Prescott Joule is famous for having measured the “mechanical equivalent of heat” in 1843 to be 838 ft·lbf/Btu. At the time this was thought of as a fundamental constant. Today, the “mechanical equivalent of heat” is 1. Since we have realized that heat and mechanical work are both manifestations of the same thing (energy) we measure them is in the same units (Joules).

    Since we know the speed of light is a fundamental constant we do not need separate units for distance and time. We keep the familiar names “meter” and “second” but really a meter is just a particular fraction of a second. We can have more units of measurement, and more fundamental constants, or fewer of both. The fashion is for fewer.

    • duffieldjohn
      October 11, 2013 at 8:38 am #

      Apologies, “crazy guys” wasn’t a good choice of words. But the people who think the speed of light is a fundamental constant are/were people like Charles Misner, Kip Thorne, John Wheeler, George Ellis, Stephen Hawking, Leonard Susskind, the list goes on. It’s the majority of people in contemporary physics. The consensus today is that the speed of light is a fundamental constant. It isn’t constant at all. That’s the whole point. Look at what Einstein said, look at the gif. See the GR section of the Baez article* and spot the contradiction. You only measure it to be constant because of the wave nature of matter. Make sure you read The Other Meaning of Special Relativity by Robert Close.

      * http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html

  4. Philip Foster
    October 10, 2013 at 8:53 pm #

    Light of course also slows down on entering a medium such as air, water or glass which is how refraction takes place.

    • duffieldjohn
      October 11, 2013 at 8:54 am #

      Refraction in glass is a little different though, Philip. Imagine you’re walking along a pavement at 4mph. If the pavement is empty, it takes you an hour to walk 4 miles. It doesn’t matter whether you’re a tall man with long slow strides or a small child with quick little steps. If you’re walking at 4mph you will travel 4 miles in one hour. That’s like the speed of light in vacuo. The speed of light in glass is like you’re walking at 4mph along a pavement with people coming at you. You have to dodge around them, hence after an hour you haven’t travelled 4 miles. You’ve travelled less. And the distance you’ve travelled does depend on whether you’re the tall man or the small child. Hence refraction in glass is frequency dependent, but gravitational lensing is not.

  5. Hunt FOR Truth
    October 20, 2013 at 3:04 pm #

    Thank you — these Sunday pages are helpful for me. I can’t say why… just being thankful
    ~ Eric

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