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Science

Single Photons Do Not Exceed the Speed of Light 196

Posted by Soulskill
from the not-quite-as-tautological-as-it-sounds dept.
GhigoRenzulli writes "A group of physicists at the Hong Kong University of Science and Technology (HKUST) led by Prof Shengwang Du reported the direct observation of optical precursor of a single photon and proved that single photons cannot travel faster than the speed of light in vacuum. HKUST's study reaffirms Einstein's theory that nothing travels faster than light and closes a decade-long debate about the speed of a single photon. ... Discovery of superluminal propagation of optical pulses in some specific medium 10 years ago has evoked the world's dream of time travel, but later scientists realized that it is only a visual effect where the superluminal 'group' velocity of many photons could not be used for transmitting any real information. Then people set their hope on single photons because in the strange quantum world nothing seems impossible — a single photon may be possible to travel faster than the speed limit in the classical world. Because of lack of experimental evidence of single photon velocity, this is also an open debate among physicists. To tackle the problem, Prof Du's team measured the ultimate speed of a single photon with controllable waveforms. The study, which showed that single photons also obey the speed limit c, confirms Einstein's causality; that is, an effect cannot occur before its cause."
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Single Photons Do Not Exceed the Speed of Light

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  • by Anonymous Coward on Monday July 25, 2011 @04:35PM (#36876110)

    QED says that the path light travels is a path of least action, one where the phasors of all the contributing paths consistently reinforce each other. Nothing in QED states that light must travel at the speed of light, it just does so because the paths where it travels at some other speed interfere with each other destructively. Over very short distance scales, light may propagate superluminally, at least, QED makes no statement that it is impossible. So this is a useful result.

    • Re: (Score:2, Informative)

      by Anonymous Coward

      Not quite, The space under which QED is valid implicitly enforces this limit on the speed of any particle. If you try doing QED on a non Minkowsi space, you will find any cross-sections you compute will be wrong.

    • by Smallpond (221300)

      Nothing in QED states that light must travel at the speed of light.

      But basic English does.

      • by lennier (44736)

        Nothing in QED states that light must travel at the speed of light.

        But basic English does.

        Oddly enough, light doesn't always travel at the speed of light, if by "speed of light" we mean "C, the fastest speed light can possibly travel" rather than "the actual speed of actual light in a medium, which is always slower than C".

        In other news, A != A for rapidly changing values of A, and zebra crossings are very dangerous places for philosophers.

    • Re: (Score:3, Interesting)

      by jasomill (186436)

      QED says that the path light travels is a path of least action

      Perhaps this is pedantry, but wouldn't that be classical mechanics? The classical "action" is mass times velocity times length, so it would vanish identically for massless particles —though modern formulations tend to substitute Hamilton's principle (discovered, incidentally, by Lagrange): admissible paths are critical points for the map from paths to real numbers given by integrating the system's Lagrangian over the path. But still, this o

    • Not true; all the field observables always commute at spacelike separations, so you can't ever send information faster than light. The propagators *do* have a non-zero amplitude at spacelike separations - it exponentially decays outside the light cone - but remember that particles are indistinguishable - you can't tell the difference between emitting a photon and absorbing it somewhere slightly off the light cone, and absorbing *some other photon*. The spacelike part of the propagator just represents corr
    • by martinX (672498)

      Nothing in QED states that light must travel at the speed of light, it just does so because the paths where it travels at some other speed interfere with each other destructively.

      Are you saying that light travels at the speed of light because it chooses too? "I could go faster, man, but, like, that'd be effort."

    • Well, they just proved that you cannot observe a photon going faster than light. Maybe photons just slow down to light speed when observed? Imagine someone setting up an experiment to "prove" that photons can only take a single path, and cannot go through two slits at the same time, by observing them and then saying "see, every single one of them went through one of the two slits!". I know I'm oversimplifying and misrepresenting things, it's just a thought.
  • Conclusion seems to be "light cannot exceed the speed of light"...

    • by blair1q (305137) on Monday July 25, 2011 @05:07PM (#36876528) Journal

      It's only called that because we haven't found a way to make it not true, yet. So no, it's not obvious, it's illuminating.

      • by grcumb (781340)

        It's only called that because we haven't found a way to make it not true, yet. So no, it's not obvious, it's illuminating.

        It's only called that because we haven't found a way to make it not true, yet. So no, it's not obvious, It's illuminating.

        I saw what you did there.

        Instantly. 8^)

    • It makes sense to have a universal constant. Light is simply a visual and measurable representation of corporeal time. Without time, we wouldn't have consciousness as there would be no movement of matter and energy. In essence, the speed of light acts as a metronome by which to judge all other forms of motion in time.

      It's quite possible that time is in fact variable outside the Universe, but we would not know that unless observing outside its influence as C would still = C from our perspective.

      • > It's quite possible that time is in fact variable outside the Universe...

        I know what you mean, if our universe were the product of a simulation computed by a 1mhz machine (with a damn lot of ram), from inside the simulation nobody could notice if the machine were upgraded to a 1ghz.

        But, to reason like this we are assuming that the concept of time is definable outside the universe, and that is an insanely big assumption.

        • Exactly.

          Strictly a thought experiment (sorry, no weed to pass around) but what if there wasn't really a Big Bang after all? What if the universe is constantly expanding as it ever was only time is slowing down exponentially. From our perspective looking back, the expansion of the universe looks like it came from a big bang. Who knows. Maybe in a bajillion years from now looking back, the last 50 billion years of the universe may have only been calculated to have happened in less than a second of their time.

          • Re:Obvious? (Score:5, Interesting)

            by Altrag (195300) on Monday July 25, 2011 @08:59PM (#36879042)

            By measuring the relative velocities of all of the galaxies, it can be extrapolated that everything (at least, everything within our visible radius) expanded from a single point. Which is not to say a central point -- for all observational purposes, the earth is the center of the universe thanks to the fixed speed of light. We can see back 13ish billion years in every direction -- there's no directional bias that would suggest we're not at the center.

            However, the same thing happens in alpha centauri as well -- they'll be able to see a few lightyears further in one direction than we can, and a few lightyears less in the opposite direction because they're also at the "center" of the universe from their perspective. Of course, we can't make use of this feature by say, having an observatory in Alpha Centauri because the time it would take for AC to send their data to us would be no less than amount of time it would take the light from that piece of the universe to reach us directly. But in as much as we can imagine a universal "now", AC will have a slightly different view of the universe than we do -- yet we're both still justified in claiming we're at the center, thus eliminating any fundamental concept of "center" beyond just calling it an observational bias.

            So back on topic, there's another couple of things that we can figure out:
            - There is stuff we cannot see. Anything beyond our past lightcone is forever lost to us unless the universe turns around and starts collapsing again. It may well be that the universe is larger, perhaps many many orders of magnitude larger than what we can observe. Its possible that our specific singularity is a minor fluctuation in some phenominally larger structure (Ekpyrotic [wikipedia.org]). But short of inventing FTL travel, we'll never be able to confirm that experimentally.

            - The universe will eventually disappear. This is a combination of the finite speed of light with eternal expansion. Eventually the expansion even between the nearest pair of "objects" will exceed the speed of light (Observable Universe [wikipedia.org]). At that point, there will simply be no universe left. I say "objects" as I'm not entirely sure at what scale gravity is able to overwhelm expansion and keep things held together. Definitely within a single galaxy, but to the scale of clusters and superclusters is something I'm less certain of. So the whole universe wouldn't disappear beyond the light cone horizon, just most of it. We're not at this point yet however -- we can see back to a time when the universe was completely opaque to light (Surface of Last Scattering [wikipedia.org]) and we'll need to develop instruments that measure gravitational waves in order to see back any further.

            - If expansion is speeding up as the big rip theory [wikipedia.org] proposes, then it will eventually get to the point where the "force" of expansion exceeds gravity, then EM and finally the strong force, ripping everything apart even down to the subatomic level and there will literally be nothing left until the next big bang.

            To sum up, we can make a pretty good estimate of how far back our observable universe goes, but whatever might be outside of our observable universe is entirely up for grabs, and the only way we can ever investigate it is to discover FTL travel, which has a very good chance of being fundamentally impossible (basically, we'd need not only new physics, but new physics that can be applied to macroscopic objects such as probes or people.)

            • So here's one that I've wondered, if the universe is expanding (that is the space in the universe), then doesn't this mean that our view of the universe is incredibly distorted, with a view of items less than 100 light years away in the same view as things 10 billion light years away, more or less giving us an inaccurate multi-time picture of the universe? The items up close are exactly where they appear to be, but the items farther away aren't anywhere close to where they appear.
              • by Altrag (195300)

                Yes, but this can be compensated for mathematically if you know the appropriate constants (primarily Hubble's constant), which we've measured with pretty good accuracy. Also, "incredibly" distorted is a bit dramatic. The force due to expansion is so tiny that its only really noticeable on the scale of hundreds of millions of lightyears. General relativity has a far greater affect on our measurements. But again, it can be compensated for mathematically.

                Of course, you get the same phenomena with simple sp

        • by lennier (44736)

          from inside the simulation nobody could notice if the machine were upgraded to a 1ghz.

          Well, as long as the simulation was entirely closed and had no I/O channels. If it did, then speed of the simulation would become measurable as we could measure it against the I/O channel's reporting of the outside world.

          In practice, almost all of our real-world computer systems do have such I/O channels, so it's not at all a given that even if the universe were a giant computer simulation, that it must be an entirely closed one...

      • > Without time, we wouldn't have consciousness as there would be no movement of matter and energy.
        Incorrect. In higher realms there is no need for space/time.

        > the speed of light acts as a metronome by which to judge all other forms of motion in time.
        For the _physical_ universes, yes. But it is not the only metronome.

    • by GodInHell (258915) on Monday July 25, 2011 @05:43PM (#36877024) Homepage
      labeling C as the "speed of light" makes the article seem like a tautology -- but C is a constant in certain theories, not a proven wall. Light often fails to travel at the speed of light, like when light is passing through air or water -- or lead (albeit not so much slower as "halted"). Take from that the following postulation: Light can vary in speed, sometimes much slower than C. Then ask this question: Does that mean that light can exceed theoretical C under the right conditions (i.e. Vacume outside the influence of gravity)? If so, what does that mean?

      I think its everything after the 'if' in that last line that explains the muddy second half of the article. (the time travel nonsense). The article does overstate the findings though -- what they did sounds pretty neat, isolating one part of the wave element of light for observation and measuring its speed in a vacum. However, observation never tells you what's impossible, only what's been observed. They have shown that the set of conditions they created support Einstein's theory. They haven't "demonstrated that light can't" do anything. They have made observations which suggests that light does not travel faster than C.

      -GiH
      • by mburns (246458)

        The relativity argument by Max Planck does fix the value of five constants of nature as determined by arbitrary human choice. Namely, physicists must decide on the magnitude of five units of measurement before they can do any measurements concerning those five constants. And it is even possible to chose units of measurement by specifying values for the five constants. (The relativistic invariant here is the physical magnitude of the constants.)

        It only remains to argue then, that the speed of light is a cons

  • "Light doesn't travel faster than the speed of light" means nothing with regard to causality. Quantum entanglement still occurs and results in faster-than-light data transmission. This doesn't disprove causality, but it sure as hell proves the speed of light has nothing to do with causality.
    • QE doesn't allow FTL data transmission. However I am still somewhat puzzled as to why FTL anything enables time travel, I mean from the wider light cone events still don't get observed before they happen, in such a way that you can manipulate the event at all. I know there is no general frame of reference, but it doesn't take much imagination to envision a frame of reference larger than your lightcone. Which you'd have to if you went FTL.

      • by Xylaan (795464)
        I've had the same question before. The best explanation that I can find is at http://www.theculture.org/rich/sharpblue/archives/000089.html [theculture.org]

        Basically, it has to do with the fact that the speed of light in a vacuum is constant, regardless of your own reference frame
      • Read "A Brief History of Time". Or wikipedia [wikipedia.org].
      • by medv4380 (1604309)
        FTL relates to time travel because of Relativity and how your speed affect how you perceive time. Basically the faster you go the slower your internal atomic clocks goes in relation to everyone elses. So if you were to get close enough to the speed of light you would experience very little if any time when you reached your destination and thus to experience time in reverse you would have to exceed that speed limit so you would have negative time. Why does it do this is your real question, and for that al
      • by blair1q (305137)

        FTL doesn't automatically imply time travel. You need to do FTL in a situation in which it implies time travel (near a rotating black hole, e.g.)

      • by beelsebob (529313)

        Because of the way that travelling distorts time. The faster you travel, the slower time passes for you relative to an observer. This means that If I set off in a jet and fly round the world, while 48 hours may pass for me, only 47 hours 59 minutes 59 seconds and some large fraction of a second will have passed for the observer stood on the ground. If I travel at the speed of light, while 48 hours may pass for me, only 0 hours, 0 minutes and 0 seconds will have passed for the observer. If I travel beyon

        • Your examples are backwards... the observes experiences more time passage than you do on your lightspeed plane, not less.

      • Your example is where relativity does not act like common experience, what happens is the person in the space ship sees the pulse move away at the speed of light, the observer sees is the spece ship and the pulse arrive at the same time.

        Quantum entanglement still occurs and results in faster-than-light data transmission

        Partly true, no information is passed FTL

        This doesn't disprove causality

        As I understand it cusality in the quantum world can be broken, eg: electron-positron pairs are spontaneously created and then promptly anihlate each other, they do this by "borrowing" energy from the immediate future and "paying it

      • by sFurbo (1361249)
        There is no universally defined "now" in a relativistic universe. Observers travelling at different speeds will disagree on whether something happens at the same time or not (see the pole-barn paradox [gsu.edu]). For every two points A and B outside of each others light cones, there is a frame of reference which sees them as simultaneous (the path is space-like), and a frame of reference that sees A as happening before B, and a frame of reference that sees B as happening before A.

        If A causes B outside it's own ligh
        • There is no universally defined "now" in a relativistic universe.

          Aren't you kinda going super relativistic with FTL? In which case "If A causes B outside it's own light cone (as it can with FTL communication), for one frame of reference, A has caused something that happened before A." has no meaning - as I said, the equations don't turn backwards, they just stop making any sense, I mean what is imaginary time? This is the point where a lot of this falls down:

          1. If you can't go FTL, you never need a frame of reference outside your lightcone therefore
          2. Causing effects out

          • by sFurbo (1361249)
            To rephrase my point: "[Y]ou can pick at most two members of the set {special relativity, causality, FTL}" (from comment by Rich [theculture.org]) Now, general relativity is a really successful theory (it explains a lot of the observations it is supposed to explain), so guessing that that is the one to go is not a good bet.

            I'm not sure what you mean by "a frame of reference outside your lightcone". If it makes my OP any easier to read, please substitute "frame of reference" for "inertial frame".
            • To rephrase my point: "[Y]ou can pick at most two members of the set {special relativity, causality, FTL}" (from comment by Rich [theculture.org]) Now, general relativity is a really successful theory (it explains a lot of the observations it is supposed to explain), so guessing that that is the one to go is not a good bet.

              Newton's laws also did a great job for a long time, in fact they still do a great job today; that doesn't mean they aren't superseded by the more recent QM for certain sets of information. I'm not saying that FTL is possible, the brute energy requirements alone would make it basically impossible to achieve. What I am saying is that FTL doesn't imply time travel as far as I can see, there's just no logical basis for it. The equations mean that relatively, time goes slower for the traveller approaching lights

              • If you have FTL and relativity (doesn't need to be General Relativity, or even Eistein's Special Relativity, it just needs to be any kind of relativity coherent with Maxell equations) there are reference frames where that FTL particles reaches its destinations before living its origin. That is what the GP is trying to say.

                We suddenly discovering that General Relativity is wrong won't change that picture, as the time and simultaniety dependence on reference frames are "big" phenomena from GR, the time depend

                • there are reference frames where that FTL particles reaches its destinations before living its origin.

                  Do you mean the FTL particles reach their destination before leaving their origin, or before light from the origin can be observed, which goes back to the idea that if it's outside your lightcone it doesn't exist? What I'm saying is that if you're looking at a faster than light frame of reference, that doesn't imply time travel, since the frame of reference is larger than your lightcone.

                  That is what the GP is trying to say.

                  We suddenly discovering that General Relativity is wrong won't change that picture, as the time and simultaniety dependence on reference frames are "big" phenomena from GR, the time dependence being tested on practice (and enough to imply the simultaniety dependence).

                  Newton's laws aren't wrong either, just sufficiently accurate for their purposes. Likewise General Relativity is almost ce

    • by ledow (319597)

      Er... no quantum entanglement ever observed/created has ever resulted in faster-than-light data transmission.

    • by Squiffy (242681)

      "Spooky action at a distance" happens faster than light, but only *after* the entanglement has been set up and the partner particle has been transmitted at light speed or slower. And even then, no information can actually be sent by this method.

  • by nimbius (983462) on Monday July 25, 2011 @04:40PM (#36876184) Homepage
    pay higher insurance premiums because theyre single, regardless of their diligent adherence to light-speed.

    that new convertible probably didnt help things either.
    • by Sloppy (14984)

      Photons are also in the most expensive age bracket too. When you look up in the sky and see a photon that has been traveling for millions of years, remember that ever since it was emitted, it has traveled at the speed of light, so no time has ever passed for it. From the photon's PoV, it was "born" in some star and then crashed (at high speed) into your retina less than an instant later.

      We see them; they don't see us. Who wants to insure that?

      • by sco08y (615665)

        Photons are also in the most expensive age bracket too. When you look up in the sky and see a photon that has been traveling for millions of years, remember that ever since it was emitted, it has traveled at the speed of light, so no time has ever passed for it. From the photon's PoV, it was "born" in some star and then crashed (at high speed) into your retina less than an instant later.

        We see them; they don't see us. Who wants to insure that?

        And how the hell will you get them to pay their premiums?

  • The universe hiding its secrets again...
  • "Speed of Light" (Score:5, Insightful)

    by bradgoodman (964302) on Monday July 25, 2011 @04:44PM (#36876248) Homepage
    By "Speed of Light" - is a constant (C). The Theory of Relativity doesn't state "light can't move faster than light" - it really states "nothing can move faster than 'C' - including light - which can travel at 'C' (in a vaccum)."

    Since light moves as fast as "C", the call "C", "Speed of Light".

    Anyway - its not really news. If they found it could move faster, that would be news!

    • by Matheus (586080)

      The title could be... "Scientists prove themselves right... again!"

      I'm firmly entrenched in the rigors of experimental science but I also firmly believe that we will one day find a way to break this "speed limit" just to rub it in the face of those who held on to the 'belief' that this observation was infallible.

      Similar to how Einstein showed us a world that behaved simply like Newton's but was really more complex, another intellect will show us one that is even more complex (or more simple). Until the nex

      • by squizzar (1031726)

        Thing is though, if we could somehow send information (for want of a better term) at a speed greater than light then we'd be able to tell our past selves just that....

    • by snowgirl (978879)

      By "Speed of Light" - is a constant (C). The Theory of Relativity doesn't state "light can't move faster than light" - it really states "nothing can move faster than 'C' - including light - which can travel at 'C' (in a vaccum)."

      Since light moves as fast as "C", the call "C", "Speed of Light".

      Anyway - its not really news. If they found it could move faster, that would be news!

      I didn't think it were particularly news either, I was all "well, duh..." and recalling the phrase from Red vs. Blue, "Can you put that in a memo and entitle it shit I already know?"

      Then I read the summary, and I remembered, oh yeah, proving our assumptions correct is useful and newsworthy as well as proving them wrong.

    • There have been numerous slashdot articles claiming that scientists have found ways to break the speed of light law. For example:
      http://science.slashdot.org/story/02/01/24/2355259/Electrical-Pulses-Break-Light-Speed-Record [slashdot.org]

      I'm not a particle physicist, but I've been extremely skeptical of such claims. The classical formula for momentum is p = m * v / sqrt (1- v^2/C^2). So, as the velocity approaches C, the upper limit for the mass approaches 0.

      The only way to accelerate a particle past the speed of light

      • You are absolutely correct.

        The other way of thinking about it - from what I have theorized (but am not smart enough to prove mathematically) - is that if you made a rocket, that was made out of pure rocket fuel, and whose engines were 100% efficient. Kind of like a 100% efficient solid-rocket-booster, whose entire self was made of it's own fuel.

        Anyway - if you were to light this thing off, (in some sort of matter/antimatteresque fashion which converted all it's mass to energy in 100% efficiency) it would

      • The only way to accelerate a particle past the speed of light is to supply it with greater-than-infinity energy, or for the mass of the particle to decrease below zero.

        I'm not going to claim otherwise, but I think the requirement can be 're-factored' as demanding a particle smaller than planck length. Such a particle could perhaps contain more energy than we observe in this universe. - Perhaps this universe was born out of the decay of such a particle. - Regardless, I seem to remember that the Standard Model had little opinion about the furthest edge of this extreme.

    • by Baloroth (2370816)

      Maybe this is true in the modern statement of Einstein's theory, but the way the theory was originally developed (at least, the way Einstein himself developed it) was that nothing could move faster than the speed of light in a vacuum, and we are going to call that c. (incidentally, its a lower case "c".) And since the way its developed also happens in this case to be the way we know things, it is very correct and true to say "nothing can move faster than the speed of light in vacuum". For convenience sake,

      • You are correct. But this is due to fact that light has no rest mass, therefore it can move at the "universal speed limit". There is nothing intrinsic to the property of light itself which makes it faster than everything else. Since it has no rest mass, it can move at the universal speed limit. If you had no rest mass, you could too.
    • by dudpixel (1429789)

      I thought the theory was that "nothing with mass can accelerate past C" ?

  • The experiment proves that under some set of conditions covered by the experiment a photon does not move faster than c. You can't automatically generalize that and claim that under no conditions does a photon exceed c.
    • by k6mfw (1182893)

      Back in the 80s someone told me he read some astronomy reports where it was observed that matter traveled faster than speed of light from huge supernova explosions. I don't think such observations been seen but I haven't spent time searching such reports. Few years ago I asked Seth Shostak of SETI, he said none have been observed traveling faster than light (the debris does move quite fast though but much slower than c).

      However, all these experiments are based on electromagnetic systems so it is all limi

  • What does "single photon with controllable waveforms" mean? I thought photons were all sinusoids under a gaussian envelope.

    • What does "single photon with controllable waveforms" mean? I thought photons were all sinusoids under a gaussian envelope.

      That would violate the superposition principle. The superposition of two arbitrary one-photon states is again a one-photon state. But the superposition of two sinusoids under a gaussian envelope is almost never a sinusoid under a gaussian envelope.

      • by Squiffy (242681)

        Ah, okay. Right. So then I guess different waveforms represent different superpositions? What is the basis? The only one I can imagine is complex exponentials, but the closest thing those have to a "location" is phase, so I don't see how they could exhibit a propagation velocity. Maybe I'm just going to have to read a book about this.

        • Do a Fourier transform of the desired waveform; the frequency-domain components are the weight of the photon state with the corresponding momentum (and polarization).
  • by glwtta (532858) on Monday July 25, 2011 @05:28PM (#36876790) Homepage
    Huh, I had no idea there was a debate about whether light travels at the speed of light.
  • Einstein's causality; that is, an effect cannot occur before its cause.

    Except here on /.
    • by lennier (44736)

      Einstein's causality; that is, an effect cannot occur before its cause.

      Except here on /.

      Sqr(-1)th post!

  • Why the only way to do time travel have to be going FTL? Couldnt be shortcuts or side approachs? Proving that one possible path won't work don't rules out any other unknown yet way to do it.

    Of course, still there is that little trouble with causality, paradoxes, and blue butterflies. But being ruled out just because that speed limit maybe isnt necessary

    • Well, of course. I am sure -though I have no knowledge of it- that back in the day people probably argued that man would never travel faster than 100mph because horses and buggies could not go that fast.

      So now we learn light apparently cannot travel faster than light, and it would be pretty difficult if not impossible to build a ship that could travel even significant fraction of that speed. Lots of energy required, blah blah blah.

      However, this says nothing about other ways yet to be discovered or inven

    • Relativity* being true, any way to FTL travel breaks causality for some reference frame.

      Independently of relativity, any way to break causality will make data travel faster than light on at least one reference frame (if you allow relativity, several reference frames).

      No shorcuts, or side approachs. If relativity is true, both concepts are equivalent.

      * Any kind of relativity coherent with the Maxell Equations. Ok, I only know about one example, but it is nice to state the requirements clearly.

  • by guspasho (941623)

    Isn't this tautological, since photons *are* light? Is this an example of yet another poor summary?

    • by guspasho (941623)

      Anon above to the rescue!

      "QED says that the path light travels is a path of least action, one where the phasors of all the contributing paths consistently reinforce each other. Nothing in QED states that light must travel at the speed of light, it just does so because the paths where it travels at some other speed interfere with each other destructively. Over very short distance scales, light may propagate superluminally, at least, QED makes no statement that it is impossible. So this is a useful result."

      ht [slashdot.org]

You see but you do not observe. Sir Arthur Conan Doyle, in "The Memoirs of Sherlock Holmes"

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