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Is a reference frame fixed to a photon an Inertial Frame?

  1. Nov 26, 2008 #1
    Hi All,

    I am a bit confused about reference frames and inertial frames.

    According to the first postulate of special relativity (if I'm right), all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform translation.

    Now if I imagine an inertial frame, from which I watch a photon -- according to the special theory of relativity -- I measure the velocity of this photon to be c. Let's call this Frame K.

    The postulate says: "there exist multiple inertial frames interrelated by uniform translation". If a translation of velocity c is a uniform one, then a frame of reference fixed to the photon would be an inertial frame as well. Let's call this Frame K'

    Here comes the dilemma which confuses me:
    In the Inertial Frame K the photon's velocity is c, like in any Inertial Frame. But how could the velocity of a photon be the same value, c, in K', which is in fact fixed to it?

    I can think of only one resolution of my dilemma:
    There's no sense of it, if we state, that any reference frame, which has a constant velocity viewing it from an inertial frame, is an inertial frame itself, except in the case when it is moving with the velocity of light, viewing it from an inertial frame.
    But by stating this (at least, for me it seams) we make the whole theory inexact.

    I think it is only a misunderstanding of the theory from my side...

    Any help would be appreciated.
  2. jcsd
  3. Nov 26, 2008 #2


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    You can create all kinds of coordinate systems where every fixed position coordinate is moving inertially and yet the coordinate system itself doesn't qualify as an "inertial frame". For example, if you have an inertial frame, and then you create a new coordinate system by doing a Newtonian Galilei transformation on it rather than the Lorentz transformation of SR, the resulting coordinate system wouldn't be an inertial frame despite the fact that every fixed position coordinate would be moving inertially. This coordinate system would violate the first postulate, since if you wrote down the equations for the laws of physics in terms of this coordinate system they wouldn't be the same equations that you get in inertial frames in SR. The first postulate would also be violated in a coordinate system where a light beam was at rest (since we know this is impossible in all sublight frames).

    It may help to realize that part of Einstein's definition of an inertial frame was a physical one describing how such a coordinate system could actually be constructed--this is the idea that an inertial observer constructs his rest frame using a grid of rulers at rest relative to himself, with clocks at each point along the rulers, the clocks synchronized by the Einstein synchronization convention. Then every event is assigned coordinates using only local readings from the ruler-marking and clock that were right next to the event as it happens (this allows you to avoid the issue of signal delays)--for example, if I see a distant explosion and I note it happened right next to the 3 light-year mark on my x-axis ruler, and the clock sitting at that mark read 15 years at the moment the explosion happened, then I would assign this event coordinate x=3 light years, t=15 years. Of course, this physical definition would make no sense for a photon, since you can't have a system of rulers and clocks moving at the speed of light (and even if you consider the limit as a system of rulers and clocks approached c, in this limit the rulers would approach being shrunk down to zero length and the clocks would approach being totally frozen, so these limiting-case rulers and clocks would be useless for constructing a coordinate system).
  4. Nov 26, 2008 #3
    Thanks for your help JesseM!

    It was my thoughtlessness...
    Clearly, I can't make use of a theory based on postulates, if I try to answer something which does not obey them. My question was illogical, I'm sorry.

  5. Nov 26, 2008 #4
    Not so illogical. Don't sell yourself short!!

    Do you know how Einstein began his research on general relativity?

    When he was sixteen, he wondered what light would look like if he caught up to and moved alongside at the same velocity....he was in essence thinking about a reference frame as you were. He was confused for a number of years until he developed special relativity when he finally concluded that space and time varied, not light speed!!!

    Thought experiments at the boundaries of understanding can be really,really useful to gain insights...Suppose the speed of light were 5c instead of just c? Suppose the speed has varied over the life of the cosmos. How do we know the speed of light isn't zero?
    and on and on...
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