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Suppose a reference frame is moving with velocity c in +x direction. An observer is there. At any time instance, another reference frame with velocity c is launched in opposite direction, i.e. -x direction. My question is what will the observer see the relative velocity of the second frame. Had the observer's velocity being anything less than c, we know according to Special Theory of Relativity it would have seen the relative velocity to be c, but what for this case? Another case of this event is seen in natural physics. We know light wave in motion, forms wavefront and at any time instance, a point on the wavefront acts as a secondary source of light. So, we consider one such case, where a secondary source is present. So, if it acts as a source, it must emit light waves in all directions, including the -x, from where the initial light came. It is the exact same event described above, where a frame with velocity -c starts moving from a frame with velocity +c. What do we see in this case?

https://www.researchgate.net/profile/Tathagata_Dey/questions

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  • $\begingroup$ Sorry Sir, but I never mentioned it to be an inertial frame. I just said a frame of reference which moves so. There is no point of inertia, when we consider velocity of light. $\endgroup$
    – Tathagata Dey
    Commented Apr 27, 2020 at 16:45
  • $\begingroup$ The special theory of relativity cannot answer this question. The singularities at $v=c$ cause the math to present no solutions. If the special theory is correct in all detail, we can conclude that no inertial frame can exist having $v=c$. The situation is non-physical, and our laws of nature would produce, if anything, nonsense. How fast can a unicorn run? $\endgroup$
    – garyp
    Commented Apr 27, 2020 at 17:01
  • $\begingroup$ If your grandmother had wheels, would she be a bicycle or a tram car? $\endgroup$
    – WillO
    Commented Apr 27, 2020 at 17:07
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    $\begingroup$ I don't think this deserves to be downvoted, it's a fair question with a legitimate answer. $\endgroup$
    – Charlie
    Commented Apr 27, 2020 at 17:10

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There is no such thing as a "reference frame moving with velocity $c$". If you use the Lorentz transformations to boost into a frame moving at the speed of light you end up dividing by zero in the gamma factor:

$$\lim_{v\rightarrow c}\frac{1}{\sqrt{1-v^2/c^2}}=\infty \tag{1}.$$

This is the point at which the mathematics of special relativity stop providing us with meaningful physical predictions. Within the framework of special relativity everything with mass (i.e. every inertial observer) is bound to travel below the speed of light. Light does not have a "frame of reference".

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There is no reference frame moving with velocity $c$. It cannot exist, because there is no frame in which an object with velocity $c$ in another frame is at rest.

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  • $\begingroup$ Yes sir, it's all hypothetical. But I am asking what will be the observations! $\endgroup$
    – Tathagata Dey
    Commented Apr 27, 2020 at 16:46
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    $\begingroup$ What you're asking is mathematically undefined and so has no physical meaning. $\endgroup$
    – Charlie
    Commented Apr 27, 2020 at 16:50
  • $\begingroup$ @TathagataDey It's not just hypothetical, it's impossible under the known laws of physics. Without a description of the laws of physics of your hypothetical universe that doesn't obey relativity, there's no well-defined answer. I could say "a sperm whale suddenly appears at the location of the observer" and it would be just as un-falsifiable as anything else. $\endgroup$
    – probably_someone
    Commented Apr 27, 2020 at 16:54
  • $\begingroup$ @TathagataDey So, if you want to make this a valid hypothetical question, you need to specify precisely how relativity is broken. For example, is the speed limit of objects infinite in this universe? How does electromagnetic radiation work? $\endgroup$
    – probably_someone
    Commented Apr 27, 2020 at 17:10

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