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Using basic logic.... We know speed and velocity is relative. My point is if we take our speed with respect to a photon moving in opposite direction we are practically moving at speed greater than that of light...... Is my argument correct?

David Z
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Shreyas Garg
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  • I don't think this is a true duplicate. While it answers part of the question (namely that addition of velocities works differently in special relativity than in Newtonian physics), but the question has more elementary problems: velocity isn't just "relative" in the sense that it depends on the point of view, but it is "relative" in that it depends on an observer, where an "observer" is defined as an inertial frame. Now one of the basic misconceptions in the question is that there cannot be an inertial frame for the photon, hence we cannot take our speed with respect to a photon. – Martin Nov 20 '15 at 14:10
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    That said, the question is answered in a combination with this question http://physics.stackexchange.com/q/16018/ – Martin Nov 20 '15 at 14:12

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No your argument is not correct. Firstly, velocities do not add linearly like 3-vectors in Euclidean space: the relativistic sum of two velocities always has a speed of less than $c$ if both the velocities' magnitudes are less than $c$ (no matter what their direction).

Secondly, photons have no rest frame: that's a basic property of things that have zero rest mass. A's speed relative to B is the speed of A measured from the frame wherein B is at rest. So let $B$ be your photon and $A$ be some other observer. But in this case, B has no rest frame. So we cannot give a meaningful answer to what $A$'s velocity relative to $B$ is. If $B$ were something other than a zero rest mass object and were moving relative to us at $c-\epsilon$ where $\epsilon$ were as small as you like, then we wouldn't run into this problem and you could calculate the relative velocity. But, as stated above, this relativistic sum cannot have a magnitude greater than $c$.

So if your question were, do we move at velocities near $c$ relative to, say, an electron accelerated to near the speed of light relative to us, then the answer would be "yes we would move at that same near to $c$ speed relative to the electron".

Selene Routley
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  • So ur basically saying that vector algebra is not applicable on bodies moving relative to speed of light and the bodies having an appreciable uncertainty of position?? – Shreyas Garg Nov 20 '15 at 15:21
  • Thanks for answer though?? – Shreyas Garg Nov 20 '15 at 15:21
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    this answer is half correct (non additionality of velocity) and half innapropriate (since in the context of the question you could replace the photon by a near-c accelerated photon). Moreover even if the text of the question says "greater than", the title says "at the speed of". So I would answer in what I think is the spirit of the question that yes, we move close to c-speed relatively to an electron moving at near c-speed. – Fabrice NEYRET Nov 20 '15 at 22:09