Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why is the speed of light the same to any observer?

  1. Mar 25, 2008 #1
    And the 2nd question:
    Do we know why is the speed of light 3*10^8 m/s? What determines this value? (I'm not asking about system of units)

  2. jcsd
  3. Mar 25, 2008 #2
    Anything that has momentum without mass is seen to travel at 'c' by any observer. This was a postulate of special relativity, and has many times been experimentally verified. If you want any more of an answer than that, you'll have to ask a philosopher. :)

    Same goes for your second question. Some have theorized that the speed of light might have changed over the life of the universe, but there's been no evidence of this.
  4. Mar 25, 2008 #3
    The value of c can be derived by postulating Maxwell's equations. The derivation shows that c = 1/sqrt(eu) where e = permitivity of free space and u = permiability of free space.

    That is a theorem (something derived) and not a postulate.

  5. Mar 25, 2008 #4
    The constancy of the speed of light was one of Einstein's original postulates. The fact that v=c when m=0 can be derived from E=pc does not make it a theorem because it already assumes that which it is trying to prove.
  6. Mar 26, 2008 #5
    My interpretation of the OP's original question is that he was asking about why c is invariant and also how the value of c is obtained. c is obtained using Maxwell's equations. The invariance of c is a postulate and as such is not derived. However we can postulate the Principle of Relativity and Maxwell's equations and then derive the invariance of c. So it really depends on what you're starting with.
    Please provide the derivation of which you speak.

    A theorem is, by definition, that which is derived from other theorems, from postulates/laws/axioms or from both. As far as E = pc then this too is something derived and not postulated. This relation can be derived from Maxwell's equatons. As such it too is a theorem. If you hold that v = 0 given m = 0 and E = pc then please proof a proof since I'm a bit uncertain as to what you're assuming as given (i.e. what are you assuming is true in that derivation?). How exactly are you defining mass m anyway?

    Definiton of theorem - a formula, proposition, or statement in mathematics or logic deduced or to be deduced from other formulas or propositions.

    If you disagree then please define the term "theorem" as you understand it and, if possible, please provide a source where you learned such a definition. Thank you.

    Last edited: Mar 26, 2008
  7. Mar 26, 2008 #6
    here is my 2 cents :
    1. constancy of speed of light wrt all observer is a postulate of relativity.
    2. Maxwells eq gives a theoritical proof of what the value should be, but doesn't imply that it is contant for all frames.
    3. even if the value of C is changing, it is same for everybody/frame at a given pint in time.

    4. to understand why it is same for all frames, if you have to deal with higher dimension. Light is actually travelling perpendicular to 4D, it is travelling in 5th dimension, but trapped by the 4D universe so that it just grazes the surface of 4D. Anything travelling in 5th dimension will not be seen as travelling with varying speed to any observer in 4D. Don't compare with X/Y axis here. XY axis is straight, where as 5th dimension is curved. Efeectively what is happening is this
    you tarvell at a speed in Y axis.
    observer is in X axis, now assume Y axis is curved although always pernedicualr to X. the component of its velocity projected on X axis will remain identical irrerespective of the movement along X axis. in eucledian X-Y axis this component is zero. in our higher dimension, where things to bend, the component is = C.

    Any object without mass, can't exist in a gravitational field, it must escape the field = escape the universe but since the higher dimensions are al curved, they graze the surface of 4D universe.

    Read kaluza-Kein theory of 5 dimension you will get the hint. If you want to know further you have to get into string theory or some such ideas.

    In fact the equations of SR can be derived from this - light is travelling perpednicular to 4D. I can't draw images here. poor at editing.
    Last edited: Mar 26, 2008
  8. Mar 26, 2008 #7
    I don't see where you get that idea from. Photons certainly exist in gravitational fields. In fact if they didn't then I'd be unalbe to read your posts. As far as remaining in a gravitational field its a well accepted notion that a photon can orbit a massive spherically symmetric body. However ther orbit is unstable.
    Nah. Unless you learn it at a layman's level then learing string theory requires an education in quantum field theory. And its a a minority of physicists know QFT. A great deal of people who post here, such as myself, have never learned string theory at a detailed level. Namely because QFT is very hard to learn. Its said to be extremely hard, if not impossible, to learn through self teaching.
    I'd have to see such a derivation before I'd believe it. Its meangless in SR to speak of light traveling perpendicular to 4d spacetime because relativity only uses 4 dimensions and having something perpendicular to spacetime requires another dimension. One then has to specify the meaning of that dimension before one can discuss it too.

  9. Mar 26, 2008 #8
    I quess your first question has 'independent of the relative speed and direction of the observer' added on the end.
    I think that it is to do with light behaving like a wave. The frequency and/or the wavelength changes (red shift/blue shift) but the relationship between these two components stays the same, hence c stays the same.

    As for the second question, I would imagine that the answer would be similar to why sound has a specific speed through water or any other medium. The only difference is that we are dealing with the natural frequency of something which has resonant inertia but is not matter.

  10. Mar 26, 2008 #9


    User Avatar
    Staff Emeritus
    Science Advisor

    I am a bit uncomforable talking about "postulates" for physics as opposed to mathematics. In mathematics we can "make up" whatever systems we want with whatever postulates we want- in physics we are constrained by reality!

    Yes, the constancy of the speed of light is a "postulate" of relativity- and it was chosen as one because that was what experimental evidence showed.

    As for why the speed of light is a constant, in Newton's immortal phrase "Hypothesen non fengo"- "I frame no hypotheses".
  11. Mar 26, 2008 #10
    I don't follow. Why do you say that we can postulate whatever we want to in mathematics? This is certainly news to me. In math the basic postulates are things like Peno's postulates, the distributive laws, the associative laws etc. But we don't make up postulates. This follows from the definition of postulate (as used in this context)

    postulate: to assume or claim as true, existent, or necessary : depend upon or start from the postulate of to assume as a postulate or axiom (as in logic or mathematics)

  12. Mar 26, 2008 #11
    This is a very good question. Turns out that light speed is set by defintion.

    The value it is set to (299,792,458m/s) was obtained averaging the results of the most recent and most precise experiments.

    Now, as to your thread title: "Why is the speed of light the same to any observer?"

    The answer has been given by others already: it is a postulate derived from multiple experimental observations. Postulates are not explainable.
    Last edited: Mar 26, 2008
  13. Mar 26, 2008 #12
    Those are not the basic posulates of math. Math has no basic postulates. Those postulates, or axioms are a set of axioms for the natural numbers. That's all they cover. There are many problems domains that go beyond natural numbers such as quantum mechanics and string theory, where the concept of addition or commutativity are not applicable.

    So using math you can develop axioms for all sorts of things, it doesn't matter, and maybe some applied mathematicians such as physicists will use them and the derived theorems to help solve their problems. But math itself certainly shouldn't concern it's self with our own experiences as HallsofIvy correctly stated.

    So in math make up whatever axiom you want and perhaps the theorems derived will cover some part of reality we have yet to know. Betrand Russel has a famous quote:

    "Thus mathematics may be defined as the subject in which we never
    know what we are talking about, nor whether what we are saying is
    true." -- Bertrand Russell
  14. Mar 26, 2008 #13


    User Avatar

    it appears that you are asking about units.

    the only fundamental physical fact imposed upon us by reality is that c is finite. it doesn't matter what the finite value is, and we may as well call it 1. the question as to why it comes out to be 299792458 m/s, is a question about units; why is the meter as long as it is (in terms of the Planck length) and why the second is as long as it is (in terms of the Planck time)?
  15. Mar 26, 2008 #14


    User Avatar

    a consequence of an even more fundamental postulate that the laws of nature are the same for all inertial observers.

    [tex] c = \sqrt{\frac{1}{\epsilon_0 \mu_0}} [/tex]

    if c were changing (or any other dimesionful "constant"), no mortal would know the difference if all of the dimensionless constants remained constant.

    of course, one would ask, if we defined the speed of light to be however fast my Toyota goes flat out on the highway, would that make it so? it's actually the meter that got defined in such a way that given the existing definition of the second, and the speed of light (how we experience and measure it), the meter is whatever length it has to be so that light travels 299792458 of them in the time elapsed by a second.

    and that was when the meter was defined as the distance between two little scratch marks on a bar of platinum-iridium (the "prototype meter" ) in the BIPM in France.

    this postulate is a little bit explainable. it really is dependent on the more fundamental postulate that the llaws of nature are the same, both qualitatively and quantitatively, for every inertial observer, even those that are moving (at constant speeds) relative to each other. it is a consequence of the very reasonable postulate that all observers that are not accelerated have equal claim to being stationary. if two inertial observers, moving relative to each other, have equal claim to being stationary (and "it's the other guy who is moving, not me") then the laws of physics, including the quantitative expression of them (two such quantities are [itex]\epsilon_0[/itex] and [itex]\mu_0[/itex] which determine c), must be identical to both observers.

    i tried to beat this horse to death in this thread.
  16. Mar 26, 2008 #15

    Yes, back in 1983.

    This is an interesting one, I have seen occasional claims of :
    -dependency of the second postulate on the first one
    (re)constructing SR based only one the first postulate

    but I could never find the respective papers/books. Do you know if the above claims are provable?

    OK, I am now going to look your horse in the mouth :-)
  17. Mar 26, 2008 #16
    If these inertial observers don't have equal claim to being stationary does Maxwell's formula become untenable?
    The reason I question it is that there is speculation about reference frames and the distortion of these near areas of high gravity. The existence of a reference frame at all may suggest that there is a theoretical 'at rest'

  18. Mar 26, 2008 #17


    User Avatar

    no, i don't think so. but if these inertial observers have unequal degrees of absolute velocity, and their absolute velocity is determined relative to some absolutely stationary frame of reference (that really doesn't exist, but we would call it "aether" if it did), then the velocities expressed in Maxwell's equations (the J vector would be charge density times a velocity vector v) and in the Lorentz force equation, those velocities would be in terms of or relative to the aether. doesn't make it untenable, just not correct.
  19. Mar 26, 2008 #18


    User Avatar

    actually, earlier than that. 1959, more like.

    depends on what you mean by "the laws of physics". if parameters that appear in the laws of physics are, themselves, part of the laws of physics, then it is an obvious logical construction to conclude that the parameters of the laws of physics (namely [itex]\epsilon_0[/itex], [itex]\mu_0[/itex], and c) remain invariant if the laws of physics are invariant.

    some people might mean that the structure of the laws of physics remaining constant do not mean that the parameters inside them must remain constant, but that is not what i mean when i say "the laws of physics remain constant" for various inertial observers. is that what Einstein meant? i think so, but someone else might disagree. but it doesn't matter because Einstein closed the door on this but explicitly stating that the laws of physics and, at least the parameter we call c, both remain invariant for all inertial observers.

    one reason i think that it is semantically silly (and logically silly) to say that the parameters inside the laws of physics aren't part and parcel to the laws of physics and do not share the same degree of invariancy as the laws of physics is that, for any particular law, let's say Newton's 2nd law, one can insert a parameter (that would be unit dependent, just like c is) initially set it to 1 (so it changed nothing, by inserting it) and hypothesize that it might vary:

    [tex] F = k \frac{dp}{dt} [/tex]

    if k varies, does that mean that Newton's 2nd law remained constant or not?

    it is no different of an issue regarding the appearance of c in the laws of physics. if the laws of physics remain invariant for different inertial observers, then i cannot see how that semantic does not mean that c, G, h, do not also. either the law, the entire law is unchanged, or it has changed.
    Last edited: Mar 26, 2008
  20. Mar 27, 2008 #19
    speed of light same for all observers

    The answer is in 'velocity measurement' here
  21. Mar 27, 2008 #20


    User Avatar
    Gold Member

    No, I think he really is asking why the speed of light is the speed that it is, independent of whatever unit you measure it in.

    Yes, you can measure the speed of light in light-seconds per second, in which case its speed is 1ls/s, or in furlongs per heartbeat. But I do think he's asking why that speed.

    I would speculate wildly that the speed was soon after the creation of the universe and is somehow related to the vacuum energy or the mass of the Higgs Boson. Or the amount of plasma vented from the warp nacelles.
    Last edited: Mar 27, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?