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How did light speed become the governor of relativity?

  1. Nov 22, 2011 #1
    Hi, I hope this is the appropriate forum.. pls move if not.

    I've been trying to learn how light "speed" found its way into relativity. Doing a bit of Googling, I found a Wiki reference that says Newton suggested that light and matter are interchangeable. As a layman, I can sort of understand how that could be, but not how light "speed" impacts on that. Somewhat like F=ma (or F=mv2), if I understood how light speed fits into the picture, I can then vaguely understand why E=mc2 works. Am I right in seeing F=mv2 as analogous to E=mc2?

    The history of such discoveries fascinates me. I'm slowly getting some of the math, but even the basics of many relativity equations still eludes me. Be patient with me.. ;)
     
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  3. Nov 22, 2011 #2

    Matterwave

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    F=mv^2 doesn't make sense. Check the units, they don't work out.

    a is not equal to v^2 in any way.
     
  4. Nov 22, 2011 #3

    atyy

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    The Principle of Relativity is that you can drink coffee in an aeroplane just as normally as you are stationary on the ground. It says if we have a frame in which the laws of physics look "standard", then the laws of physics will look the same in another frame moving at constant velocity relative to the first. The Principle of Relativity implies that the laws of physics have symmetry.

    Newton's laws have a symmetry called Galilean invariance which implements the Principle of Relativity.

    Research in electricity and magnetism by Ampere, Faraday and others led Maxwell to formulate his equations governing electromagnetism and light. It was noticed that Maxwell's equations don't have Galilean symmetry.

    Does this mean the Principle of Relativity is violated? No. Maxwell's equations have a different symmetry called Lorentz invariance or Poincare invariance. That symmetry is also consistent with the Principle of Relativity.

    Although the Principle of Relativity is consistent with both Galilean and Lorentz invariance, it is not consistent with them co-existing. This led Einstein and Planck to modify Newton's laws so that they had Lorentz invariance. Galilean and Lorentz invariance are indistinguishable at low speeds, which is why we had not noticed that Newton's laws are only approximate for more than 200 years.

    It is possible that Lorentz invariance is also approximate. However no experiment has yet detected its failure.
     
  5. Nov 22, 2011 #4

    ghwellsjr

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    Maybe in order to close the loop on the OP's question, you should have explicitly pointed out that Galilean invariance does not have the speed of light in it whereas Lorentz invariance does.
     
  6. Nov 22, 2011 #5

    D H

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    This is a huge point. It made for a huge schism in physics at the end of the 19th century, much greater than today's schism between general relativity and quantum theory. Our schism is theoretical only. While physicists don't know how to rectify general relativity and quantum theory yet, physicists have not (as far as I know) detected a direct conflict between the two. On the other hand, the conflict between Maxwell's electrodynamics and Newtonian mechanics was not just a theoretical schism. It had been directly observed in experiments and confirmed in follow-on experiments.

    Because it was such a deep schism, the best minds of the time worked on rectifying the two. One approach was to view the problems as pertaining to electromagnetic radiation only. This approach led to a rather unsatisfactory theory of relativity. It isn't taught today. Einstein chose to take Maxwell's equations at face value: The speed of light is the same to all observers. This simple acceptance of the basic concept shouted out by Maxwell's equations coupled with the relativity principle (the laws of physics are the same in all inertial frames) yields special relativity.

    In hindsight, special relativity was there for any of the other people working in the area to see. They didn't see it because they couldn't let go of the cherished principles of Newtonian mechanics.
     
  7. Nov 22, 2011 #6

    atyy

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    A side note: in fact there is not even a theoretical schism between GR and quantum theory. Our present view is that the standard model of particle physics is only an effective theory, with QED and the Higgs sector likely to fail at a very high energies. GR can be similarly incorporated into quantum theory as an effective field theory. I'm not entirely certain, but I believe GR is expected to fail at an energy above which the Higgs sector fails, but below which QED fails. This explains why there is no conflict between GR and particle physics.
     
  8. Nov 22, 2011 #7

    robphy

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    That sounds like a particle-physics view of GR as merely a field theory in Minkowski spacetime. However, a relativist's view would emphasize a curved-spacetime [with possibly nontrivial topologies], which looks Minkowskian in a small neighborhood.

    What do you mean by "quantum theory" (which is distinct from "particle-physics")?

    I think current formulations of "GR" and "quantum theory" have foundational differences, which is one of the reasons why Quantum Gravity hasn't been properly formulated yet.
     
  9. Nov 22, 2011 #8

    D H

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    Sorry, that "quantum theory" was my terminology. Some of ya'll get tweaked at calling the standard model etc. "quantum mechanics". To me they are all variations on the same non-classical theme, but that's perhaps because that entire part of my physics education has atrophied from lack of use. (I've been working as an aerospace engineer and systems engineer for the last 30+ years.)
     
  10. Nov 22, 2011 #9

    atyy

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    Yes, the formulation I had in mind assumes trivial spacetime topology. It further assumes that spacetime can be covered with harmonic coordinates (apparently, this assumption can be weakened if I correctly understand a comment in Weinberg's text, but I have never seen that elaborated). As I understand, there isn't observational evidence that requires one to go beyond these. I believe harmonic coordinates can penetrate the event horizon. Also, the equivalence principle can be derived in this framework, whereas minimal coupling isn't a real principle of GR, only background independence.

    Well, I'm a biolgist, so I'm even more clueless about this. Weinberg does say that QM is more important than QFT, from which I gather he considers QFT a type of QM. In condensed matter, there is an exact equivalence between non-relativistic QM and non-relativistic QFT (roughly it's just a Fourier transform). So I think you were right on this.
     
    Last edited: Nov 22, 2011
  11. Nov 23, 2011 #10

    ghwellsjr

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    How do Maxwell's equations shout out that the one-way speed of light is the same to all observers?
     
  12. Nov 23, 2011 #11
    Actually, the speed of light is not properly named !!!

    It should be named the "invariant speed".
    And it happens that any zero-mass particle can only travel at the invariant speed.
    It happens that it is also the speed of light. (photons have no mass)

    Historically, light offered physicist the opportunity to discover the "invariant speed".
    This is why it was called like that.
    To be honest, still today, light is by far the best thing to measure this "invariant speed".
    The recent FTL neutrinos story shows that quite well.
    Also, very fast electrons in accelarators could be use to observe the "invariant speed", but in a much more difficult way.
     
    Last edited: Nov 23, 2011
  13. Nov 23, 2011 #12
    Thanks everyone for your answers.. :)

    Oops.. I was getting confused with the formula for centrifugal force.

    This actually makes some sense to this novice.

    Did Newton suggest that matter is interchangeable with light (or one can be converted to the other)? It made me think that, if that's so, then that would make light speed the "invariant speed" of matter, especially if there's no loss in the conversion. Kind of like if all the energy in a sample of matter is converted to light, then light speed represents some limit of the energy in that matter. I can't explain exactly how I think this other than it seems intuitively correct. And if so, then that would mean that the energy of a mass would be proportional to some factor of light and the size of the mass. Is that how E=mc2 came about?
     
  14. Nov 24, 2011 #13

    D H

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    You're thinking of Einstein, not Newton. And Einstein did not say that matter is interchangeable with light. He said that mass is a form of energy. Slight difference there.

    What lalbatros was getting at was that a better name for the speed of light is the invariant speed of the universe. All photons must travel at c, not just the photons that happen to be in the visible range. More importantly, all massless particles must travel at c, not just photons. So calling c the speed of light is a bit restrictive. But it's the name we're stuck with.

    Besides, "invariant speed of the universe" is a bit too wordy while "speed of light" is nice and succinct.
     
  15. Nov 24, 2011 #14
    I got the info from this Wiki article:
    "In 1717 Isaac Newton speculated that light particles and matter particles were inter-convertible..."
    Thanks for the clarification, it does help. :)

    What I'm trying to understand, is how we got to the understanding of this "invariant speed". People have shown me λ calculations, which I've struggled to follow. I'm trying to understand the historical path. As I understand it at the moment, these steps may have been part of the journey:

    1) Someone (Newton?) discovered the "inter-convertible" nature of light particles and mass particles. (How? I know of his experiments with light and prisms, but what led to his "speculation"?)
    2) Sometime later, c was determined to be the max speed of anything in the universe. (How? And did it have something to do with "inter-convertibility" demonstrating max energy from matter or something of that nature?)
    3) Did 1 and 2 impact on Einstein coming up with E=mc2? And is there a lay way of explaining it?
     
  16. Nov 24, 2011 #15

    A.T.

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    It was determined experimentally. It was contradicting the simple Galilean transformation. So they had to find another transformation that keeps the speed of light unaffected:

    https://www.youtube.com/watch?v=C2VMO7pcWhg
     
  17. Nov 24, 2011 #16

    D H

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    That is not a good way to see it.

    A massive object can never go at c. No matter how much energy is added to massive object (relative to some observer), that observer will never see the object moving at c. A better way to think of E=mc2 is that it is a lower bound on energy, not an upper bound. An object with zero velocity relative to some observer still has energy given by E=mc2. There is no upper bound on energy in special or general relativity.
     
  18. Nov 25, 2011 #17
    The youtube video was wonderfully illustrative. The three effects made sense (shrinks moving objects, slows down moving clocks, breaks simultaneity) with the shrinking of moving objects being a great surprise.

    How did they come to understand the need to keep the speed of light unaffected? Please excuse the ignorance, as I had wondered if it is a bit like how sound is compressed then stretched, like when an aircraft passes overhead, and possibly also accounts for Doppler effect.
     
  19. Nov 25, 2011 #18

    A.T.

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    That's simply what you observe in the real world. The speed of EM-waves doesn't depend on the speed of the source. So the very same photon has the same speed in every inertial frame.
    No, because sound has uniform speed only the rest frame of the medium. EM-waves have a uniform speed in all inertial frames.
     
    Last edited: Nov 25, 2011
  20. Nov 25, 2011 #19

    Dale

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    The title of the thread makes me laugh. I keep picturing c and γ in a presedential-style debate. Each asking supporters to contribute to their campaign, running vicious adds accusing the other of ties to Newtonian physics, and having illicit relationships with coordinates, etc. Finally the election results lead to a narrow victory for c who becomes the newly-elected governor of relativity.
     
  21. Nov 25, 2011 #20
    Hi,

    I was just wondering if "in a vacuum" is an essential part of the constant, C.
    If Dark matter exists, doesn't this make a vacuum something that only exists in a laboratory, if anywhere at all? If there is no vacuum then there is no constant, if there is no constant ...

    or is "c" just a mathematical concept like natural e
     
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